This paper introduces a fully distributed model-free adaptive control method, addressing the tracking problem for multiple-high-speed trains (MHSTs) featuring sensor resolution and utilizing round-robin protocol. Sensor resolution is one of the basic characteristics of almost all sensors and an important indicator of sensor performance in practical applications, but it has not been given enough attention in the study of MHSTs. Since MHSTs have unknown dynamical properties, firstly, the dynamic linearisation technique is used to obtain the data relation description of MHSTs. Secondly, to address the issue of data transmission pressure caused by limited network bandwidth in Train-to-Train (T2T) direct communication, the round-robin protocol can be adopted for effective alleviation. On this basis, a distributed model-free adaptive control strategy is proposed to achieve the bounded formation tracking of MHSTs with sensor resolution under the round-robin protocol. Finally, the effectiveness of the proposed control scheme is verified by simulation examples.

This paper investigates a data-driven finite-time cooperative control problem for nonlinear multi-agent systems (MASs) and develops a distributed model-free adaptive prescribed-performance control strategy based on partial-form dynamic linearization (PFDL). First, a finite-time prescribed performance function is introduced to transform the distributed output errors, ensuring that the prescribed performance constraints are satisfied. Next, an improved dynamic linearization method is derived to convert the transformed error dynamics into an equivalent linear data-driven model, which facilitates controller synthesis. On this basis, a finite-time performance index is constructed and a distributed model-free adaptive cooperative control algorithm is proposed. Moreover, a dual-channel event-triggering mechanism with separate triggering rules for control inputs and measured outputs is designed to reduce the communication burden. Rigorous analysis establishes finite-time convergence of the distributed output errors and boundedness of the control inputs. Numerical simulations demonstrate the effectiveness and robustness of the proposed method.

In this work, a new adaptive predictive iterative learning control (APILC) scheme is designed for a class of multiple-input-multiple-output (MIMO) discrete-time nonlinear systems, which simultaneously addresses the problems of randomly varying iteration lengths, iteration-time-varying system uncertainties on parameters and disturbances, iteration-time-varying reference trajectories, and system constraints. First, in order to compensate for missing output/state data caused by randomly varying iteration lengths, a new search decision compensation mechanism (SDCM) is constructed to select optimal data from historical data, estimated data, and predicted data, thereby mitigating the impact of randomly varying iteration lengths on the tracking performance. Next, a new adaptive learning algorithm is developed based on the compensated data, which not only estimates and predicts iteration-time-varying system uncertainties on parameters and disturbances, but also constructs a more accurate adaptive prediction model to effectively capture future dynamic characteristics of the system. Furthermore, the constructed adaptive prediction model is employed to design an APILC scheme that simultaneously handles both iteration-time-varying reference trajectories and system constraints. Theoretically, the convergence of both the adaptive prediction model and the tracking error is rigorously guaranteed, even under system constraints and various iteration-time-varying operating environments. Ultimately, the simulation results verify the effectiveness of the proposed SDCM based APILC (SDCM-APILC) scheme.

This work aims at developing a novel direct design and analysis method of learning control protocol toward consensus performance of multiagent systems (MASs) without using any model. A nonlinear autoregressive moving average (NARMA) function is designed at first to formulate the inherent consensus dynamics with respect to the consensus error and the control protocols. Then, a consensus performance-related iterative linear data model (CPiLDM) is constructed for equivalently reformulating the NARMA consensus system's iterative dynamics in a data-driven framework. The CPiLDM does not rely on a model no matter through first-principle modeling or system identification methods. Next, a direct distributed iterative learning control (DirDILC) method is developed through an optimization technique subject to the CPiLDM. The convergence is proved directly for the virtual NARMA consensus system, without relying on the dynamics of the agent itself, and thus simplifies the analysis consequently. Since the presented DirDILC is purely data-driven without relying on an explicit model, it constitutes a significant step forward from the existing consensus control theory.

In this article, a novel model-free adaptive fuzzy control (MFAFC) scheme is proposed to tackle the frequency fluctuation issue in complex interconnected power systems under sensor measurement and input saturation constraints. Communication between sensors and controllers is facilitated through a shared network, with the Round-Robin protocol employed to manage data transmission and prevent collisions.First, the Takagi-Sugeno (T-S) fuzzy system with a local nonlinear model is used to represent the multi-area interconnected nonlinear power system. Subsequently, the dynamic linearization technique is employed to describe the data relationships within each subsystem of the T-S fuzzy power system. Based on this data model, an model free adaptive fuzzy control algorithm is developed, and the convergence of tracking errors is thoroughly analyzed. To assess the control performance, a three-area interconnected power system is selected as the test case. Simulation results demonstrate that the MFAFC scheme effectively mitigates frequency fluctuations, showcasing its robust tracking performance and reliability.

The security tracking control problem is addressed for nonlinear discrete-time networked control systems (NCSs) subject to energy-constrained denial-of-service (EC-DoS) attacks. A probabilistic quantization-based coding-decoding protocol (CDP) is designed to mitigate bandwidth limitations and enhance transmission security. Then, a CDP-based data-driven adaptive sliding mode control (DDASMC) method is presented on the basis of a linear data model (LDM) of the nonlinear NCSs. A detection algorithm is designed to detect EC-DoS attacks so that the proposed CDP-based DDASMC can automatically switch between two cases with and without EC-DoS attacks, respectively. In the duration that the attack does not occur, an integral sliding function and a reaching law are designed to achieve fast convergence while ensuring a good control performance. In the duration that the attack occurs, a prediction mechanism is introduced to construct a predictive LDM for estimating future control information. Further, a sliding mode predictive control is developed to address the EC-DoS attacks and enhance the control performance. All the algorithms of the proposed DDASMC are computed only using the input-output (I/O) data instead of any other information of the physical models. Simulation study validate the results.

This study addresses the challenge of precise control of the maglev system under the condition of rapid time-varying dynamics and large time delay. Maglev technology has been applied in many fields, such as maglev train and magnetic bearing, for its non-contact operation, low maintenance cost and high energy efficiency. However, the inherent nonlinear characteristics and delayed response characteristics of the magnetic levitation system make it very difficult to control. In practical scenarios, it is difficult to establish an accurate magnetic suspension system model, which limits the use of model-based control methods. PID control method is also difficult to guarantee the control performance when dealing with unmeasurable load disturbance and system delay scenarios. This study proposes a data-driven control solution, which integrates an optimized recursive identification algorithm and an adaptive delay compensation algorithm. Uniquely, the control solution achieves real-time iterative optimization with only a few input and output data, reducing the data storage resource requirements, avoiding offline training, and ensuring real-time performance and efficient resource utilization in practical applications. Practitioners can use this new method to enhance the performance and reliability of maglev applications, such as maglev trains, industrial processes and precision instruments, so as to achieve more robust and adaptive control in the face of rapid dynamic changes and large time delays. Note to Practitioners—This study addresses the challenge of precise control of the maglev system under the condition of rapid time-varying dynamics and large time delay. Maglev technology has been applied in many fields, such as maglev train and magnetic bearing, for its non-contact operation, low maintenance cost and high energy efficiency. However, the inherent nonlinear characteristics and delayed response characteristics of the meglev system make it very difficult to control. In practical scenarios, it is difficult to establish an accurate magnetic suspension system model, which limits the use of model-based control methods. PID control method is also difficult to guarantee the control performance when dealing with unbearable load disturbance and system delay scenarios. This study proposes a data-driven control solution, which integrates an optimized recursive identification algorithm and an adaptive delay compensation algorithm. Uniquely, the control solution achieves real-time iterative optimization with only a few input and output data, reducing the data storage resource requirements, avoiding offline training, and ensuring real-time performance and efficient resource utilization in practical applications. Practitioners can use this new method to enhance the performance and reliability of maglev applications, such as maglev trains, industrial processes and precision instruments, so as to achieve more robust and adaptive control in the Phase of rapid dynamic changes and large time delays.

This paper considers the problem of containment control for multi-input multi-output (MIMO) nonlinear multi-agent systems (MASs) with output saturation and aperiodic denial-of-service (DoS) attacks. By applying the dynamic linearization method, the nonlinear systems are modified to an equivalent linear data model. Based on the inputs and saturated outputs data, a new data-driven containment control algorithm in the presence of aperiodic DoS attacks is developed, which mainly includes the following perspectives: 1) based on the historical information of the MASs, a switched error system is designed to decrease the impact of aperiodic DoS attacks, where the time duration was constrained due to the limitation of attackers’ energy; 2) the relation between measured error and tracking error is constructed to deal with the difficulties of incomplete data suffered from output saturation; 3) with the help of contraction mapping method and mathematical induction approach, the boundedness of containment error is guaranteed by the convergence of the control strategy in such an insecure environment. Numerical simulations are given to validate the effectiveness of the framework. Note to Practitioners—This paper studies the containment control problem for MIMO nonlinear MASs, which has application value in robotic systems, intelligent transportation, multiple spacecraft systems, and other fields. Note that these systems are notably susceptible to network attacks and saturation nonlinearity, which may decrease the system performance or even cause instability. Since the agent dynamics generally are not accurate even unavailable, the existing model-based technologies are inappropriate for MIMO nonlinear MASs. Therefore, in light of the challenge aroused by aperiodic DoS attacks and output saturation, a novel switched error system-based model-free adaptive containment control approach is developed to preserve data integrity while the stability of containment error is guaranteed. Numerical simulations indicate the validity of the obtained results.

This paper proposes a novel model-and-data-driven adaptive frequency control (MDAFC) for microgrid (MG) systems. The proposed MDAFC includes two control loops, i.e., an adaptive model predictive control (AMPC) loop and a model free adaptive control (MFAC) loop. The AMPC loop not only utilizes the exact model information to improve the control performance but also employs an unscented Kalman filter (UKF) to estimate the unknown parameters of the internal prediction model to improve the robustness to a certain degree. The MFAC loop is designed to address the unmodeled dynamics, nonlinear uncertainty and disturbance of the MG system by virtue of its adaptation mechanism and the data-driven characteristics. Therefore, the MFAC loop can compensate the poor impact of the inaccuracy model information on the AMPC method. To validate the effectiveness of the proposed method, a low inertia MG system containing renewable energy sources (RESs) is considered in this research. Simulation results show that the proposed method can achieve a high control performance. It can effectively cope with the frequency fluctuation caused by RESs, large load consumption, and other unknown uncertain factors. Compared with the existing single AMPC loop and the single proportional integral control loop, the proposed dual-loop-based MDAFC performs better since the two control loops cooperate with each other to leverage their advantages and compensate for their shortcomings.

Overhead cranes are important transportation equipments in practice, however, their existing control methods have encountered many difficulties in applications due to the underactuation, input limitation and computation complexity. This paper proposes an adaptive fixed-time control scheme for the underactuated overhead crane with multiple uncertainties to deal with the above challenges simultaneously. A coordinate change is employed to address the underactuated structure by reformulating the crane dynamics as a strict-feedback system. A series of time-varying tuning functions are designed to guarantee the input signal varies within a small range to meet the practical input requirement of the overhead crane system. Moreover, a second-order nonlinear tracking differentiator (NLTD) is set up to avoid the repetitive derivative calculation of the virtual controllers. Then, an adaptive law is designed to tackle multiple uncertainties with no need of introducing any other control algorithms but only the single one of itself. Further, a light computational adaptive fixed-time control scheme is proposed by consisting of the tuning functions, NLTD, and the adaption law to achieve a fast location of the overhead crane system. The simulation experiments illustrate the effectiveness of the presented method.

This paper addresses the output feedback fixed-time consensus tracking problem for nonlinear multiagent systems (MASs) subject to aperiodic DoS attacks and actuator faults. Different from existing resilient control methods for MASs where the attackers only destroy the connectivity between agents, the sensor-to-controller communication channels of each agent are simultaneously blocked in this paper. To overcome these difficulties, we first propose a novel fixed-time stability criterion that incorporates the characteristics of DoS attacks. Then, a fuzzy state estimator is constructed to estimate the immeasurable states as well as compensate for the adverse impact of attacks. In addition, novel adaptive laws are developed to handle an infinite number of actuator failures by estimating the bounds of failure parameters. Based on the Lyapunov stability theory, a fixed-time output feedback resilient control strategy is designed to guarantee that consensus tracking can be achieved, while the boundedness of all closed-loop signals in the MAS is ensured. At last, simulation studies are performed to validate the performance of the designed control law.Note to Practitioners—Many real-world systems, including robotic systems, manipulator systems and intelligent vehicle systems, can be represented as strict-feedback MASs. Note that these systems are notably susceptible to network attacks and operational faults. Consequently, ensuring the continued functionality of controlled MASs with DoS attacks and actuator faults has emerged as a paramount research focus. Furthermore, in the context of systems necessitating high transient performance standards, the concept of fixed-time convergence holds practical significance. In light of the challenges posed by DoS attacks and actuator faults, a novel fixed-time fuzzy fault-tolerant resilient consensus tracking approach is designed for nonlinear MASs. The proposed control laws cater to practical MASs which are characterized in strict-feedback form subject to unknown nonlinearities. Preliminary simulation results indicate the feasibility and efficacy of our developed approach.

For cooperative control of multiple high-speed trains (MHSTs), a new model free adaptive predictive iterative learning cooperative control (MFAPILCC) method is proposed in this paper. Firstly, the unknown nonlinearity of the MHSTs is handled with the full form dynamic linearization (FFDL) technology along the iteration domain. Then with the predictive mechanism, the unknown bounded time-iteration-varying external disturbances are estimated and predicted, and also be incorporated into the controller design, which achieves better disturbance rejection and system stability. Specially, under the proposed MFAPILCC method, apart from the convergence of tracking error of system could be guranteed, the modeling error of system which practically makes a difference in the cooperative tracking performance of MHSTs also could be guranteed to converge to zero. The convergence of the modeling error and speed tracking error of the system under the constructed method could be guranteed through rigorous theoretical derivation, while the distance between adjacent trains is always maintained within a safety range. Finally, a simulation on the Chinese Railway High-Speed Train (CRH-3) operation control system is supplied to validate the efficacy and superiority of the proposed MFAPILCC method for cooperative control of MHSTs. It is obvious that the theoretical justification and simulation effects either reflect efficacy of the proposed MFAPILCC method.

Considering the three critical factors of data quantization, channel fading, and denial of service (DoS) attack introduced by the networked control systems (NCSs) simultaneously, we propose a novel compensatory data-driven networked iterative learning control (COMP-DDNILC) method for nonlinear repetitive NCSs under a model-free design and analysis framework. By reformulating the iterative input-and-output (I/O) dynamics of the nonlinear NCS as an iterative linear data model (iLDM), an iterative linear predictive data model (iLPDM) is developed to predict the missing data arisen from DoS attacks. Then, a relationship is built to describe the coupling effects of the three critical factors, based on which the COMP-DDNILC is designed by involving the compensatory mechanism of DoS attacks and the fading coefficient inversion to improve the control performance. The COMP-DDNILC also involves an iterative adaption mechanism to update the iLPDM to enhance the robustness against uncertainties. The data-driven nature of COMP-DDNILC makes it applicable to practical NCSs without model information available. The simulation study verifies the results.

This article considers the point-to-point tracking control problem for a class of unknown nonlinear discrete-time systems with output saturation. A novel data-driven finite-iteration learning control algorithm is proposed to achieve bounded tracking errors within limited iteration. First, considering the case that the model of the nonlinear discrete-time system is unknown, the relationship between the output of the system and the control inputs at these given points is derived using recursive evolution in the time domain. Then, the dynamic data-driven model of the system is established using iterative domain dynamic linearization techniques. Second, a finite finite-iteration learning algorithm based on the fractional power of error information is designed, and the finite-iteration convergence of the proposed algorithm is rigorously proven in theory. Finally, the effectiveness of the proposed method is validated by simulation results.

The actuator faults and channel fading are unavoidable in the nonlinear continuous-time MIMO multiagent systems (MASs), which significantly complicate the formation control problem. To tackle these challenges, a model-free adaptive fault-tolerant formation control (MFAFTFC) scheme based on the sampled-data full-form dynamic linearization (SD-FFDL) technology is proposed, which integrates the data-based formation control algorithm, the fuzzy neural network algorithm, and the projection algorithm. The stability analysis of MFAFTFC scheme is strictly provided. Simulation comparison results with unmanned ground vehicle demonstrate the effectiveness of the proposed MFAFTFC scheme, that is, the proposed MFAFTFC scheme can achieve the formation objective for the nonlinear continuous-time MIMO MASs subjected to actuator faults and fading channels.

This article provides a new methodology to design a novel predictive control (PC) scheme for unknown nonlinear discrete-time systems, by deeply exploiting future ideal controllers and the dynamic linearization (DL) technique. The control input increment vector can be linearly parameterized with the time-varying control gain vector. The PC law is obtained by directly optimizing the control gain vector with the least square method. The system outputs are predicted through the parameterized PC law and the DL data model of the controlled system. The proposed PC scheme is data-driven, that is, it does not depend on the system dynamic model and the control gain vector is adaptively optimized by using only the measured input/output data. The monotonic convergency of the proposed PC scheme is theoretically guaranteed, and its effectiveness is validated by two illustrative examples, i.e., a complicated nonlinear system and a linear time-invariant system.

This article aims to address the problem of distributed model-free adaptive iterative learning control for nonlinear discrete-time multiagent systems under switching topologies. To save valuable bandwidth in the wireless channel without sacrificing system performance, an event-triggered iterative learning control strategy is established and employed, where information is only transmitted at triggered instants. First, by virtue of the dynamic linearization technology, the controlled system can be converted into a linear model to construct the controller structure. Second, a model-free adaptive iterative learning consensus control scheme is proposed merely employing the input and output data, in which better tracking performance can be attained by learning the previous experience. Third, a dynamic event-triggered mechanism along the iteration domain is set up to deal with the limited bandwidth issue, effectively saving communication resources. Unlike most model-free adaptive control results, the constructed distributed controller is designed based on controller-dynamic-linearization approach to deal with the controller structure design issue without designing the cost function, making it more convenient in solving tracking control issues for multiagent systems under iteration-switching communication topologies, which is more suitable for the actual environment. Using graph theory and the contraction mapping principle, the convergence of tracking control errors is theoretically analyzed. Ultimately, the effectiveness of the established control schemes is illustrated through two simulation examples.

This paper studies a multiple-input multiple-output fuzzy adaptive data-driven security control issue for multiple-unit high-speed train (HST) with actuator faults and dynamic sensor attacks. Firstly, the ideal controller of HST is modified to an equivalent linear data model by utilizing the dynamic linearization method. Then, a novel partial form dynamic linearization controller-based model-free adaptive control framework is designed. To alleviate the impact of actuator faults, the unknown fault-related uncertainties are approximated by employing a fuzzy logic system (FLS), and the fuzzy weight is estimated by introducing a parameter estimation criterion function. Furthermore, a fixed threshold sensor attack detection mechanism is introduced to detect and isolate compromised sensors by predicting the speed of the train in the next time interval. Based on the prediction algorithm, an improved data fusion strategy is developed to compensate for the impacts of sensor attacks, which can remove the requirement of the number of attacked sensors while allowing the system to maintain robust performance under various attack conditions. It is shown that the proposed algorithm is effective in the sense of the generic norm, thus ensuring reliable and safe operation for the multiple-unit HST. Eventually, simulation examples are provided to confirm the proposed protocol.

In this paper, an enhanced model-free adaptive control algorithm considering time delay is proposed for the path tracking problem of autonomous vehicles. First, a path tracking mechanism based on the preview-deviation-yaw angle is proposed, which transforms the path tracking problem into a control problem of the preview-deviation-yaw angle. A novel partial form dynamic linearization (PFDL) technique is then employed to transform the vehicle dynamic models into a discrete-time data model with a time-varying pseudogradient (PG), and the proposed controller (PFDL-EMFAC) is designed based on this data model. Moreover, a compensation mechanism is designed for the system time delay by combining the Smith predictor and tracking differentiator (TD). Notably, implementing the controller does not involve any model information; it is a purely data-driven control method. Furthermore, the convergence of the proposed controller is proven via mathematical analysis. The validity of the proposed controller was validated through CarSim-MATLAB cosimulation, and its applicability was verified via the Ankai HFF6668GEV1 autonomous driving platform on a test road in Hefei, China.

This paper studies a hierarchical distributed model-free adaptive control issue for heterogeneous multiple high-speed trains with random deception attacks. By employing the dynamic linearization method, the high-speed train systems are modified to an equivalent linear data model. Then, a novel hierarchical distributed model-free adaptive security control framework is designed mainly including the following perspectives: 1) an adaptive distributed observer is devised for each train to estimate the virtual reference signal; 2) by employing the local information, a decentralized control scheme is developed to ensure that every train can track the reference velocity and position trajectories; 3) a deception attacks detection and compensation strategy is designed to determine whether the received data is attacked or not and compensate for the false signals. The system stability is rigorously proven via the contraction mapping technique and mathematical induction method where the speed and position tracking of heterogeneous trains is guaranteed. Eventually, a simulation example is provided to verify the effectiveness of the proposed protocol.

This paper investigates the issue of speed tracking and dynamic headway adjustment for multiple subway trains (MSTs) under data dropouts. First, the nonlinear subway train system is transformed into a disturbance-related full-form dynamic linearization (dFFDL) data model. Second, based on the obtained dFFDL data model and the asynchronous event-triggered mechanism, the model-free adaptive event-triggered predictive cooperative control (MFAETPCC) algorithm is proposed, utilizing only the input/output and disturbance data of MSTs to compensate for data dropouts, reduce the communication and computation burden, and ensure control performance. As a result, theoretical analysis reveals that the speed tracking errors of MSTs are bounded and the distances of adjacent trains are kept within a safe range. Finally, the effectiveness of the proposed MFAETPCC algorithm for MSTs is demonstrated by simulation results.

This paper aims to develop the RBFNN-based data-driven fast terminal sliding mode control for nonlinear multiagent systems (MASs) subjected to unknown uncertainties and external disturbances. First, a multiagent system with unknown uncertainties and external disturbances is transformed into a full-form dynamic linearization (FFDL) data model. Then, the RBFNN algorithm is utilized to compensate for the complex unknown nonlinear terms encountered by unknown uncertainties and external disturbances, and the data-driven fast terminal sliding mode control is designed to realize the finite-time consensus tracking and enhance the robustness of MASs. Finally, a simulation test applied to subway trains is conducted to demonstrate that the proposed RBFNN-based data-driven FTSMC algorithm is characterized by high tracking accuracy.

This article proposes a sampled-data fault-tolerant bipartite formation control (SD-FTBFC) algorithm that incorporates the sampling period and historical input and output data for nonlinear continuous-time multi-input-multioutput (MIMO) multiagent systems (MASs) subjected to unknown sensor faults. First, a sampled-data full-form dynamic linearization data model employing the principles of differential and integral mean value theorems is established to address the unknown nonlinearities of the continuous-time MASs. Afterward, a time-varying fault detection threshold is developed to ascertain the occurrence of sensor faults. Subsequently, the unknown sensor faults are approximated by the fuzzy neural network algorithm, and the uncertain parameters of MASs are tackled by the projection algorithm. A rigorous stability analysis for the proposed SD-FTBFC algorithm is thoroughly presented. Ultimately, the simulation outcomes utilizing multiple unmanned ground vehicles confirm the efficacy of the proposed SD-FTBFC algorithm.

This article investigates fully distributed robust adaptive Nash equilibrium (NE) seeking strategies in noncooperative games. Different from existing NE seeking results, this article considers high-order nonlinear multiagent systems (MASs) with mismatched uncertainties and disturbances. To deal with the challenges brought by the high-order structure, a new auxiliary system is first introduced based on the gradient play rule to generate a reference trajectory, which converges to the NE exponentially without requiring any global graph information. Then, a backstepping-based robust adaptive controller is developed for each agent to exponentially track the reference trajectory. By resorting to the Lyapunov stability theory, the developed robust seeking strategies drive all agents’ actions to the NE exponentially. Moreover, considering the circumstance that only the information of the agent’s action is available for control law design, an adaptive output-feedback NE seeking strategy is further developed by constructingK-filters to estimate the immeasurable states. Finally, the effectiveness of the two proposed NE seeking algorithms are verified by different simulation examples.

This article focuses on the problem of dual-channel event-triggered (ET) adaptive neural network (NN) fixed-time (FXT) optimal consensus for nonlinear multiagent systems (MASs) with unknown control directions. A dual-channel ET FXT tracking strategy is applied to address the FXT optimal consensus problem. First, to save communication resources, ET mechanisms are designed for both the sensor-to-controller (S–C) channel and the controller-to-actuator (C–A) channel. In addition, to deal with the nondifferentiability issue of the virtual controllers caused by the ET mechanism, a switching transformation function is designed to reconstruct the output signals. Based on the reconstructed signals, an FXT control algorithm is devised by utilizing the backstepping technique, where the Nussbaum functions are designed to compensate for the negative impact of unknown control directions. Then, the actor-critic architecture-based reinforcement learning (RL) technique is implemented at each step to generate optimal control commands, ensuring optimal performance while ensuring consensus tracking. With the Lyapunov stability theory, it is verified that the designed control algorithm can guarantee the achievement of consensus tracking in a fixed time. Finally, the effectiveness of the designed algorithm is demonstrated by a representative simulation.

This paper studies the prescribed-time tracking problem for nonlinear systems with an uncertain parameter leader. Due to the important role of leaders in the tracking controller design, a leader dynamic observer with the prescribed-time performance is firstly designed to estimate the uncertain leader system while ensuring that the estimation error can approach the origin in the pre-given finite time. In addition, due to the presence of the uncertain parameter leader dynamics in the virtual controller, the derivative of the virtual controller is unknown, which makes the backstepping technique unusable. Thus, a novel filter is constructed by combining with the prescribed-time function to avoid using the virtual controller derivative in the tracking controller design.Further, based on the estimated leader dynamics, an adaptive fuzzy prescribed-time tracking control strategy is proposed by using the backstepping approach, which enables the system output signal can track the uncertain leader without errors in the pre-given finite time. Finally, the vitality of the developed controller is checked by an actual example with comparisons.

This paper considers a prescribed performance-based event-triggered model-free adaptive control (ET-MFAC) problem for nonlinear system without and with false data injection (FDI) attacks. First, the nonlinear system is converted into an equivalent linear data model by utilizing the dynamic linearization technique. Then, the event-triggered constrained tracking control schemes for nonlinear system without and with FDI attacks under the data-driven framework are designed, which include the following three parts: 1) a prescribed performance function and converted output signal are directly employed in the cost function, and the constraint control schemes are derived by the cost function to realize the prescribed performance requirement; 2) an event-triggered mechanism is designed on the basis of the relationship between measurement error and tracking error, which can decrease the communication burden; 3) in order to reduce the negative effect of FDI attacks on nonlinear system, a resilient security control scheme is presented. Finally, a numerical example shows the efficiency of the developed control methods without and with FDI attacks.Note to Practitioners—This paper investigates an event-triggered constrained tracking error control for the nonlinear system without and with FDI attacks. To avoid utilizing accurate model information, MFAC is introduced into the design process of presented strategies. Incorporating prescribed performance control with an event-triggered mechanism, the developed constrained tracking strategy is designed for the first time to lessen the computational burden while improving the transient and steady-state performance on system. Moreover, based on the energy constraint of FDI attackers, a novel resilient security constrained tracking strategy is developed to decrease the impact of FDI attacks on considered nonlinear system. The validity of theoretical results is carried out by a simulation.

For a class of unknown MIMO non-affine nonlinear repetitive discrete-time systems, a novel data-driven high-order point-to-point iterative learning control scheme is proposed. The control input objective function of this method consists of two parts. One includes the high-order error information, the other consists of the control inputs within the time sub-intervals divided by prescribed desired points. The control law is designed by optimizing this function and it comprises only the known control input signals in the current iteration and the error data in previous iterations. Further, the convergence analysis is conducted in a data-driven way and does not need precise mathematical models. In addition, a scalar index function is set up to evaluate the tracking error convergence rate. By choosing the appropriate high-order factor and corresponding step-size factors, the convergence rate of higher-order learning law is shown to have a faster speed than that of lower-order one. Simulation experiments verify the effectiveness and advantage of this method.Note to Practitioners—The motivation of this paper is to design a control algorithm that only depends on the information of the prescribed desired points, that is, the point-to-point iterative learning control scheme. This control algorithm can be competent for terminal temperature control tasks with very intense chemical reactions and other control tasks that the information except for the I/O data at the prescribed desired points is unavailable. When we want to improve further the control performance at some prescribed desired points, the data of some intermediate time instants can be used to supply extra support for the control system design to improve the control performance at the prescribed desired points. In fact, the point-to-point iterative learning control scheme can be applied to many fields, such as high-speed trains, functional electrical stimulation areas, and positioning X–Y tables. In this paper, a data-driven high-order point-to-point iterative learning control scheme for the MIMO systems is designed, and the stability of this scheme is theoretically analyzed by using the contraction mapping method. Further, the tracking error convergence rate with different order learning law is analyzed. Finally, two numerical simulations are used to verify the effectiveness of the scheme proposed in this paper.

A model free adaptive iterative learning control based fault-tolerant control (MFAILC-FTC) scheme for subway train speed tracking with speed sensor fault and over-speed protection is proposed. Firstly, the train dynamics is transformed into a compact form dynamic linearization (CFDL) data model by applying the concept of pseudo-partial derivative (PPD). If speed sensor fault occurs, the fault function is approximated by the trained RBFNNs under normal condition and the output data of the train system with fault, which serves as a compensation for the proposed MFAILC-FTC scheme. Then, over-speed protection mechanism is developed to ensure that the train operates within safe speed range. Furthermore, the constraint on traction/braking force is also taken into account. Through rigorous mathematical analysis, it is proved that the proposed MFAILC-FTC method with over-speed protection mechanism can ensure the train speed tracking error converges along the iteration axis, which implies the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm. Note to Practitioners—Subway train as a practical engineering system with short distance between two stations, starts and stops frequently, has the outstanding repetitive operation pattern, and it is unavoidable subject to speed sensor fault, aerodynamic issues, constraint on output speed and traction/braking force. Nevertheless, few works have considered these factors simultaneously, and a lot of data contain valuable operation information are generated during the train operation, this motives the work of this note. On account of the repetitive operation features of subway trains, the control schemes of speed trajectory tracking are handled under MFAILC framework, which is a pure data-driven model free control methodology. By constructing the RBFNNs-based fault function estimation mechanism, a robust compensation term is designed in the fault-tolerant controller. Taking the safe operation of subway trains into account, an over-speed protection term with trigger mechanism is added to the fault-tolerant controller. To further enhance the application, the constraint on traction/braking force is addressed as well. Without requirement of the train dynamics model, the theoretical analyses and simulation results have confirmed the effectiveness and the feasibility of the proposed data-driven control approach. In the future work, we will focus on verifying the proposed control strategy and addressing some other practical problems, for instance, the energy-efficiency and exogenous disturbances during the train operation.

In this paper, we consider the need for deployment in the long-distance safe longitudinal formation control task when the connected autonomous vehicle (CAV) platoon is subjected to malicious cyber attacks. To ensure the safe, orderly, stable and efficient driving performance of the vehicle platoon, a novel distributed data-driven control (DDDC) approach for a homogeneous connected autonomous vehicle platoon under false data injection (FDI) attacks is investigated. First, an FDI attacks detection and compensation mechanism is designed to detect whether the received position signals are under attack or not and compensate the attacked position signals. Then, a novel DDDC approach for the vehicle platoon longitudinal formation control is developed by using the compensation data from the designed attack compensation mechanism and a dynamic linearization data model. Theoretical analysis verifies that the proposed DDDC method can ensure the internal stability (IS) and string stability (SS) of the homogeneous platoon subjected to FDI attacks. Finally, the effectiveness and practicality of the proposed DDDC approach are validated through a group of comparative simulations subjected to random FDI attacks of equal frequency and magnitude.Note to Practitioners—This work aims to solve the vehicle platoon long-distance safe longitudinal formation control task subjected to malicious FDI attacks. FDI attacks can achieve their destructive purposes by processing intercepted information and injecting false data into the original information. Existing literature overly relies on a priori knowledge of network attacks, yet in practice it is difficult to capture the true intentions of attackers in advance. For multi-channel V2V communication networks, it is even more important to design a resilient and accurate distributed controller strategy for such unpredictable and specific network attacks. Therefore, this paper proposes a data-driven distributed longitudinal formation control strategy with attack detection and compensation mechanism. The proposed strategy is shown to be able to ensure the safe longitudinal formation control task for the homogeneous CAV platoon suffering from FDI attacks. In addition, the stability of the CAV platoon is then investigated while the attacked signals are detected and cleaned, and it is shown to guarantee the internal stability of a single vehicle and the string stability of the platoon.

For discrete-time nonlinear systems with uncertainty, this paper presents an interval analysis approach to design controller and compute the estimate of the closed-loop robust domain of attraction (RDOA). The dynamics of the system is modelled using difference inclusions. A robust negative-definite and invariant set (RNIS) in the state-control space is proposed. An RNIS is defined by the combination of a robust negative-definite set (RNS) and a robust controlled invariant set (RCIS), which leads to sufficient conditions for Lyapunov stability of the system. The estimate of RDOA can be obtained by projecting an RNIS along the state space. However, the RNIS is hard to obtain by its definition. Drawing inspiration from the RCIS-computation approach, we define a mapping that utilizes the predecessor operator in the state-control space to compute a set limit. Then, the RNIS can be obtained by finding the limit set for an RNS. The computations of RNS and the limit set are based on interval analysis. An algorithm to estimate the RNIS is introduced with rigorous convergence analysis. Finally, we formulate an optimization problem that is solvable, and enlarges the RNIS and the estimate of RDOA. The method is validated on examples of nonlinear systems subject to actuator saturation.

This work aims at presenting a new sampled-data model-free adaptive control (SDMFAC) for continuous-time systems with the explicit use of sampling period and past input and output (I/O) data to enhance control performance. A sampled-data-based dynamical linearization model (SDDLM) is established to address the unknown nonlinearities and nonaffine structure of the continuous-time system, which all the complex uncertainties are compressed into a parameter gradient vector that is further estimated by designing a parameter updating law. By virtue of the SDDLM, we propose a new SDMFAC that not only can use both additional control information and sampling period information to improve control performance but also can restrain uncertainties by including a parameter adaptation mechanism. The proposed SDMFAC is data-driven and thus overcomes the problems caused by model-dependence as in the traditional control design methods. The simulation study is performed to demonstrate the validity of the results.

A data-driven dynamic internal model control (D3IMC) scheme is proposed for unknown nonlinear nonaffine systems bypassing modeling steps. Different from the traditional internal model constructed by either a first-principle or an identified model, a dynamic internal model (DIM) is developed in this work using I/O data where a compact form dynamic linearization approach is introduced for addressing the nonlinearity and nonaffine structure. Then, the D3IMC is proposed with both a nominal control algorithm and an uncertainty compensation control algorithm. The former can quickly respond to the feedback errors and the latter can compensate the model-plant mismatch and external disturbances. Meanwhile, the adaptive parameter updating law in the proposed D3IMC method inherits the robustness against uncertainties. A nominal D3IMC is also designed without including the compensator when there is no exogenous disturbance since the adaptive mechanism can handle system uncertainty. Further, the results are extended and a full-form dynamic linearization-based D3IMC is developed to address control of nonlinear systems with more complex dynamics. All the proposed D3IMC methods are data-driven without need of an explicit model, and thus they are significant extensions from the traditional model-based IMC. Simulation study verifies the results.

A novel learning-based model-free adaptive control (LMFAC) approach is presented in this article for a class of unknown nonaffine nonlinear discrete-time networked control systems (NCSs) subject to hybrid cyber attacks. The aperiodic denial-of-service (DoS) attacks and persistent deception attacks are assumed to arise in feedback channels, which could result in the absence or authenticity lackness of system signals sent to the controller. With the aid of dynamic linearizaton technology, the equivalent dynamic linearized data models of considered NCSs are first established only based on I/O information instead of the knowledge of mathematical models that are commonly used under the model-based control framework. Then, an LMFAC scheme is designed on the basis of occurred maximum DoS attacks interval to adaptively tune the attenuation coefficient of the input signal for improving system performance during the next DoS attacks interval. Finally, the boundedness of tracking error is rigorously proved through the contraction mapping principle and the effectiveness of the proposed pure data-driven LMFAC method is demonstrated via simulations.

In this article, a disturbance observer dynamic linearization (DL)-based model-free adaptive control (MFAC) scheme is proposed for discrete-time nonlinear systems with disturbances and uncertainties. The partial-form-dynamic-linearization-based disturbance observer (PDO) is constructed by applying the DL method to an unknown ideal disturbance observer. An adaptive updating algorithm of the observer gain is derived by minimizing a estimation criterion function. Then, the PDO-based MFAC scheme is formed and its bounded stability is rigorously analyzed using the contraction mapping principle. The proposed scheme is a purely data-driven control method, that is, both the PDO and control system are designed by using only the input/output data of underlying system. A numerical simulation and a vehicle turning experiment are given to verify the effectiveness of the proposed scheme.

A novel reinforcement learning (RL)-based model-free adaptive control (MFAC) strategy is proposed to address the consensus tracking control issue for multiagent systems subjected to data injection attacks launched in the communication channel. By virtue of the dynamic linearization technique, equivalent dynamic linear data models for nonlinear systems and unknown linear ideal controllers are provided with the aim of determining the controller structure. Meanwhile, to reduce the effects of injection attacks, the fuzzy logic system is used to approximate the unknown nonlinear function by an online learning approach. Moreover, an RL MFAC method is proposed by employing the actor-critic structure to optimize the parameter estimation performance. Rigorous proofs are presented to ensure that the closed-loop systems are uniformly ultimately bounded even in the presence of injection attacks. The validity and superiority of the provided algorithm are further demonstrated through representative simulations.

This article addresses a finite-time prescribed performance-based model-free adaptive control (MFAC) issue for vehicular platooning systems under aperiodic denial-of-service (DoS) attacks. By applying the dynamic linearization method, the nonlinear vehicular platooning systems are modified to an equivalent linear data model. Based on the inputs and outputs data, a new finite-time data-driven prescribed performance control algorithm with aperiodic DoS attacks is developed, which mainly includes the following perspectives: 1) a smooth shifting function is employed to circumvent the restriction of initial conditions that demand the initial values of tracking errors be within a preset area; 2) by introducing a finite-time performance function (FTPF) into cost functions, the constrained outputs are transformed into an equivalent unconstrained condition; 3) based on historical information of the systems, a compensation mechanism is designed to decrease the influence of incomplete data aroused by aperiodic DoS attacks. The proposed algorithm guarantees the prescribed performance control within a finite time under insecure circumstances. Eventually, the proposed protocol is verified by detailed simulations.

This paper investigates a distributed data-driven event-triggered fault-tolerant control for a connected heterogeneous vehicle platoon with sensor faults under the vehicle-to-vehicle (V2V) communication network. First, a sensor fault diagnosis scheme based on the high-gain observer is designed to detect, estimate and compensate for the fault signal. Then, the measurement signals with sensor faults are recovered, and the reconstructed system can be modeled by the full-form dynamic linearization (FFDL) technique. To obtain reliable vehicle data communication with the efficient use of network resources, an event-triggered mechanism based on the formation error is established, and then a distributed data-driven controller can be designed to accomplish the platoon formation control task. Theoretical analysis demonstrates that the proposed distributed event-triggered fault-tolerant control method can realize the task of ensuring the safe formation control of the platoon system under some sensor faults. Finally, a simulation of a platoon with three faulty vehicles is made to verify the effectiveness and real-time performance of the proposed method.

This article presents an adaptive iterative learning fault-tolerant control algorithm for state constrained nonlinear systems with randomly varying iteration lengths subjected to actuator faults. First, the modified parameters updating laws are designed through a new defined tracking error to handle the randomly varying iteration lengths. Second, the radial basis function neural network method is used to deal with the time-iteration-dependent unknown nonlinearity, and a barrier Lyapunov function is given to cope with the state constraint. Finally, a new barrier composite energy function is used to achieve the tracking error convergence of the presented control algorithm along the iteration axis with the state constraint and then followed with the extension to the high-order case. A simulation for a single-link manipulator is given to illustrate the effectiveness of the theoretical studies.

This article develops a novel data-driven finite-iteration learning control (DDFILC) for the nonlinear repetitive systems that are stable for the finite operation length. Both the error range and the finite-iteration number can be designated beforehand by considering the efficiency and economy of the industrial processes. As a result, not only can the proposed DDFILC guarantee the desired product quality but also can reduce the operation cost. First, a linear data model (LDM) is constructed to reformulate the system dynamics that satisfies the Lipschitz continuity condition. Then, an iterative updating law of the DDFILC is developed for estimating the unknown parameter of the LDM. The proportional-differential type learning law used in the DDFILC has two iteration-time-varying learning gains, both of which are updated according to the linear matrix inequality conditions. Not only the finite-iteration convergence but also the iteratively asymptotic convergence can be shown mathematically by using the two-dimensional (2-D) system theory. The proposed DDFILC approach does not require an exact model and is robust to uncertainties. The simulation study verifies the results.

The leaderless or leader-following consensus tracking, along with containment control problems of nonlinear multiagent systems (MASs) using controller-dynamic-linearization-based distributed model-free adaptive control (CDL-DMFAC) method are addressed in this article. By virtue of dynamic linearization (DL) technology, the distributed output and ideal controller of MASs are first converted to the corresponding equivalent DL data models, respectively. Then, a pure data-based CDL-DMFAC scheme is uniformly constructed by employing I/O data regardless of the state space model of MASs. The convergence analysis is rigorously proved by a designed data energy function without using global topology graph information. Furthermore, the control strategy and convergence result are extended to acrlong MIMO MASs. Finally, extensive simulations are performed to verify the validity of theoretical results.

The event-triggered model-free adaptive predictive control (ET-MFAPC) problem for a class of networked nonlinear control systems (NCSs) under deception attacks is addressed in this article. By using dynamic linearization technology, the NCSs are converted to an equivalent data model, and a networked MFAPC scheme with an adjustable input decay rate is constructed to compensate for the network delay. Meanwhile, the attack phenomena existing in feedback channels are modeled by considering both multiplicative and additive deception factors. Then, an ET mechanism without long-time dormancy behavior is proposed to reduce the calculation burden of the controller and save network communication resources. Rigorous convergence analysis for the proposed pure data-driven ET-MFAPC algorithm is given by employing the contraction mapping principle and it shows that the boundedness of tracking error in the mean-square sense can be guaranteed under the presented ET-MFAPC scheme. Finally, extensive simulations are performed to verify the theoretical results.

In this work, a model-free adaptive containment control scheme is investigated for a class of multi-input multi-output nonlinear multiagent systems, where the agents’ dynamics are unknown with output saturation. Firstly, the dynamics of followers are transformed into a equivalently data model by using full form dynamic linearization technology. Secondly, the distributed containment control algorithm is proposed only using the input data and the saturated output data of followers and neighbors. Further, the boundedness of the containment error is proved by using the contraction mapping principle and mathematical induction method. It is shown that the developed scheme can ensure that the followers move into the convex hull composed of the leaders. Last, the effectiveness of the developed scheme can be verified through numerical simulations.

In this paper, we present a novel approach to address the event-triggered optimized consensus tracking control problem in a class of uncertain nonlinear multi-agent systems (MASs). To optimize control performance, we employ an adaptive reinforcement learning (RL) algorithm based on the actor-critic architecture and utilize the backstepping method. The proposed RL-based optimized controller employs a novel event-triggered strategy, dynamically adjusting sampling errors online to reduce communication resource usage and computational complexity through the intermittent transmission of state signals. We establish the boundedness of all signals in the closed-loop MAS through stability analysis using the Lyapunov method, and demonstrate the prevention of Zeno behavior. Numerical simulations of a practical multi-electromechanical system are provided to validate the effectiveness of the proposed scheme.

This article considers the problem of fixed-time prescribed event-triggered adaptive asymptotic tracking control for nonlinear pure-feedback systems with uncertain disturbances. The fuzzy-logic system (FLS) is introduced to deal with the unknown nonlinear functions in the system. By constructing a new type of Lyapunov function, the restrictive requirement that the upper bounds of the partial derivative of the unknown system functions need to be known is relaxed during the controller design process. At the same time, by developing a novel fixed-time performance function (FPF), the fixed-time prescribed performance (FPP) can be achieved, that is, the tracking error can converge to the neighborhood of the origin in a fixed time and finally converges to zero asymptotically. In addition, the event-triggered strategy is developed to reduce the waste of communication resources. The proposed control law can ensure that all the signals of the system are bounded. Meanwhile, the Zeno behavior can be effectively avoided. Finally, an example is provided to prove the effectiveness of the proposed scheme.

This article proposes a data-driven distributed filtering method based on the consensus protocol and information-weighted strategy for discrete-time sensor networks with switching topologies. By introducing a data-driven method, a linear-like state equation is designed by utilizing only the input and output (I/O) data without a controlled object model. In the identification step, data-driven adaptive optimization recursive identification (DD-AORI) is exploited to identify the recurrence of time-varying parameters. It is proved that for discrete-time switching networks, estimation errors of all nodes are ultimately bounded when data-driven distributed information-weighted consensus filtering (DD-DICF) is executed. The algorithm combines with the received neighbors and direct or indirect observations for the target node to produce modified gains, resulting in a novel state estimator containing an information interaction mechanism. Subsequently, convergence analysis is performed on the basis of the Lyapunov equation to guarantee the boundedness of DD-DICF estimate error. Simulations verify the performance of the DD-DICF against the theoretical results as well as in comparison with some existing filtering algorithms.

In this article, a higher order indirect adaptive iterative learning control (HO-iAILC) scheme is developed for nonlinear nonaffine systems. The inner loop adopts a P -type controller whose set-point is updated iteratively by learning from the iterations. To this end, an ideal nonlinear learning control law is designed in the outer loop. It is then transferred to a linear parametric-learning controller with a corresponding parameter estimation law by introducing an iterative dynamic linearization (IDL) method. This IDL method is also used to gain an iterative linear data model of the nonlinear system. A parameter iterative updating algorithm is utilized for estimating the unknown parameters of the obtained linear data model. Finally, the HO-iAILC is presented that utilizes additional error information to improve the control performance and employs two iterative adaptive mechanisms to deal with uncertainties. The convergence of the proposed HO-iAILC scheme is proved by using two basic mathematical tools, namely: 1) contraction mapping and 2) mathematical induction. Simulation studies are conducted for the verification of the theoretical results.

This article investigates the issue of speed tracking and dynamic adjustment of headway for the repeatable multiple subway trains (MSTs) system in the case of actuator faults. First, the repeatable nonlinear subway train system is transformed into an iteration-related full-form dynamic linearization (IFFDL) data model. Then, the event-triggered cooperative model-free adaptive iterative learning control (ET-CMFAILC) scheme based on the IFFDL data model for MSTs is designed. The control scheme includes the following four parts: 1) the cooperative control algorithm is derived by the cost function to realize cooperation of MSTs; 2) the radial basis function neural network (RBFNN) algorithm along the iteration axis is constructed to compensate the effects of iteration-time-varying actuator faults; 3) the projection algorithm is employed to estimate unknown complex nonlinear terms; and 4) the asynchronous event-triggered mechanism operated along the time domain and iteration domain is applied to lessen the communication and computational burden. Theoretical analysis and simulation results show that the effectiveness of the proposed ET-CMFAILC scheme, which can ensure that the speed tracking errors of MSTs are bounded and the distances of adjacent subway trains are stabilized in the safe range.

In this article, an improved model-free adaptive control (iMFAC) is proposed for discrete-time multi-input multioutput (MIMO) nonlinear systems with an event-triggered transmission scheme and quantization (ETQ). First, an event-triggered scheme is designed, and the structure of the uniform quantizer with an encoding-decoding mechanism is given. With the concept of partial form dynamic linearization based on event-triggered and quantization (PFDL-ETQ), a linearized data model of the MIMO nonlinear system is constructed. Then, an improved model-free adaptive controller with the ETQ process is designed. By this design, the update of the pseudo partitioned Jacobean matrix (PPJM) estimates and control inputs occurs only when the trigger conditions are met, which reduces the network transmission burden and saves the computing resources. Theoretical analysis shows that the proposed iMFAC with the ETQ process can achieve a bounded convergence of tracking error. Finally, a numerical simulation and a biaxial gantry motor contour tracking control system simulation are given to illustrate the feasibility of the proposed iMFAC method with the ETQ process.

This paper addresses the event-triggered model free adaptive control (MFAC) problem for unknown nonlinear systems under denial-of-service (DoS) attacks, where the design and analysis are discussed under the data-driven framework. Firstly, by using the novel pseudo partial derivative, the nonlinear systems are converted into an equivalent data-relationship model. Then, the DoS attacks are described as limited by their frequency and duration, and without any more specific assumptions about the attack structure or strategy. Next, a novel event-triggered MFAC scheme is proposed. By employing the Lyapunov stability theory, the stability performance is analyzed. Furthermore, a compensation algorithm is designed to against the adverse impact brought by the DoS attacks. Finally, simulations including a numerical example and a load frequency control (LFC) example for multi-area power systems are given to demonstrate the validity and applicability of the proposed schemes.

In this study, a data-driven adaptive iterative learning Kalman consensus filtering (DD-AILKCF) method is designed for high-speed trains to address the parameter identification and speed consistent optimal estimation problem. The nonlinear train dynamics model is transformed into a linear-like state-space model by using the Full Form Dynamic Linearization (FFDL) technique. Meanwhile, four types of sensors are used to obtain different kinds of datasets to implement the multi-sensor system. The method proposed in this paper consists of two steps. First, an adaptive iterative learning Kalman filtering (AILKF) algorithm is proposed to estimate the fast-time varying train parameter in the iteration domain. Then, based on the identified parameter, a distributed multi-source heterogeneous network consensus filtering (MHN-CF) algorithm is proposed for the speed estimation of high-speed trains. The convergence of the proposed algorithm is derived based on the Lyapunov Function. The proposed method is compared with existing methods by numerical simulations, and the results indicate that the proposed method achieves good effectiveness in improving the accuracy of high-speed train speed estimation.

An extended state observer based model-free adaptive iterative learning energy-efficient control (ESO-based MFAILEEC) scheme for subway train speed tracking with external disturbances and over-speed protection under the constraint on traction/braking force is proposed. Firstly, the continuous-time train motion dynamics is formulated into a discrete-time data model with consideration of external disturbances by applying the iterative dynamic linearization. Meanwhile, the external disturbances and the unknown nonlinear uncertainties of the train are transformed into a new state, which is estimated by an ESO designed in the iteration domain. Then, the ESO-based energy-efficient controller with learning ability is designed, which enables the train to achieve the purpose of energy efficiency by reducing the input force. Further, over-speed protection with trigger mechanism is developed to ensure the train operates within safe speed range. All the control strategies are designed under the constraint on traction/braking force by considering the practical limitation of the train system. No model information is involved in the whole design processes and it is a pure data-driven iterative learning approach. Rigorous mathematical analysis proves the feasibility and the robustness of the proposed method, which can guarantee the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm.

A data-driven spatial adaptive terminal iterative learning predictive control (SATILPC) scheme with actuator saturation is proposed for automatic stop control of the subway train. Considering the outstanding repetitive operation pattern and the unavailable accurate model of a subway train, the unknown train dynamics is firstly transformed into a nonlinear discrete form in spatial domain via the spatial differential operator. Since the train automatic stop control (TASC) only concentrates on the tracking performances of the terminal position and terminal speed, an iterative dynamic linearization approach considering the terminal operation point is devised to formulate the relationship of the train input and output (I/O) into a linear affine form. Then, a terminal iterative learning prediction mechanism is introduced to reconstruct the developed train data model to forecast the future train behaviors through rolling optimization process. As a result, by removing the constraints on the unimportant points, the optimal control input (braking force) can be obtained by minimizing the objective function through terminal I/O data. Further, actuator saturation is considered to address the passenger comfort and the reliable operation of the train. The proposed SATILPC approach is a pure data-driven iterative learning control scheme and no model information is involved in the whole design processes. By utilizing a newly space-based contraction mapping method, the convergence of the proposed approach is strictly proved. Finally, the simulation results further demonstrate the feasibility of the proposed algorithm.

Heterogeneous dynamics, strongly nonlinear and nonaffine structures, and cooperation-antagonism networks are considered together in this work, which have been considered as challenging problems in the output consensus of multiagent systems. A heterogeneous linear data model (LDM) is presented to accommodate the nonlinear nonaffine structure of the heterogeneous agent. It also builds an I/O dynamic relationship of the agents along the iteration-dimensional direction to make it possible to learn control experience from previous iterations to improve the transient consensus performance. Then, an adaptive update algorithm is developed for the estimation of the uncertain parameters of the LDM to compensate for the unknown heterogeneous dynamics and model structures. To address the problem of cooperation and antagonism, an adaptive learning consensus protocol is proposed considering two signed graphs, which are structurally balanced and unbalanced, respectively. The learning gain can be regulated using the proposed adaptive updating law to enhance the adaptability to the uncertainties. With rigorous analysis, the bipartite consensus is proven in the case that the graph is structurally balanced, and the convergence of the agent output to zero is also proven in the case that the graph is unbalanced in its structure. The presented bipartite consensus method is data-based without the use of any explicit model information. The theoretical results are demonstrated through simulations.

The bipartite formation control for the nonlinear discrete-time multiagent systems with signed digraph is considered in this article, in which the dynamics of the agents are completely unknown and multi-input multi-output (MIMO). First, the unknown nonlinear dynamic is converted into the compact-form dynamic linearization (CFDL) data model with a pseudo-Jacobian matrix (PJM). Based on the structurally balanced signed graph, a distance-based formation term is constructed and a bipartite formation model-free adaptive control (MFAC) protocol is designed. By employing the measured input and output data of the agents, the theoretical analysis is developed to prove the bounded-input bounded-output stability and the asymptotic convergence of the formation tracking error. Finally, the effectiveness of the proposed protocol is verified by two numerical examples.

This article systematically addresses the distributed event-triggered containment control issues for multiagent systems subjected to unknown nonlinearities and external disturbances over a directed communication topology. Novel composite distributed adaptive neural network (NN) event-triggering conditions and event-triggered controller are raised meanwhile. Furthermore, the designed event-triggered controller is updated in an aperiodic way at the moment of event sampling, which saves the computation, resources, and transmission load. On the basis of the NN-based adaptive control techniques and event-triggered control strategies, the uniform ultimate bounded containment control can be achieved. In addition, the Zeno behavior is proven to be excluded. Simulation is presented to testify the effectiveness and advantages of the presented distributed containment control scheme.

The consensus tracking and containment control problems of multiple-input and multiple-output (MIMO) nonaffine nonlinear multiagent systems (MASs) are studied in this article under deception attacks using the distributed model-free adaptive control (DMFAC) method. An equivalent dynamic linearized data model of MIMO MASs’s distributed output vector containing deception signals is established using dynamic linearization technology. Then, a fully data-driven DMFAC strategy is designed just using I/O information instead of the knowledge of mathematical model. Furthermore, the boundedness of distributed output vector of MIMO-MASs under deception attacks is proved through the contraction mapping principle without employing global topology graph information. Finally, the validity of the proposed DMFAC scheme is verified through detailed simulations.

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

For the consensus tracking of multiagent systems (MASs), most of existing distributed control methods need to design the controller structure with availability of physical model or structural information of each agent, which is sometimes impractical due to the difficulty of modeling each agent or obtaining its structural information if the physical model of each agent is complicated and the underlined MAS is heterogeneous. To handle this issue, in this article we first integrate the controller-based dynamic linearization method into distributed control using only the local measurement information exchanging among neighbors in a directional graph and the input of each agent. Then we propose a data-driven distributed adaptive control (DAC) method for nonlinear nonaffine heterogeneous discrete-time leader–follower MASs. We show that the proposed method has ultimately bounded tracking error in both of the cases with fixed and switching communication topologies. The numerical simulation results show that in contrast with two DAC methods, the proposed one can give smaller tracking errors.

This article investigates the problem of event-triggered model-free adaptive iterative learning control (MFAILC) for a class of nonlinear systems over fading channels. The fading phenomenon existing in output channels is modeled as an independent Gaussian distribution with mathematical expectation and variance. An event-triggered condition along both iteration domain and time domain is constructed in order to save the communication resources in the iteration. The considered nonlinear system is converted into an equivalent linearization model and then the event-triggered MFAILC independent of the system model is constructed with the faded outputs. Rigorous analysis and convergence proof are developed to verify the ultimately boundedness of the tracking error by using the Lyapunov function. Finally, the effectiveness of the presented algorithm is demonstrated with a numerical example and a velocity tracking control example of wheeled mobile robots (WMRs).

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

This article reconsiders the data quantization problem in iterative learning control (ILC) for nonlinear nonaffine systems from four aspects: 1) use of available additional control knowledge; 2) different tracking tasks; 3) adaptation to uncertainties; and 4) data-driven design and analysis framework. An iterative linear data model (iLDM) is established first to represent the nonlinear nonaffine system for subsequent control algorithm design and analysis under a data-driven framework. A quantitative data-driven adaptive ILC (QDDAILC) is then developed using quantized tracking errors based on the nonlifted iLDM and, thus, additional available input information from previous time instants can be utilized to improve control performance. The parameter estimation derived from an adaptive updating law makes the learning gain of the QDDAILC adjustable, therefore improving the robustness to uncertainties. Due to the coupled dynamics among inputs and tracking errors, a new double-dynamics analysis method is introduced besides the contraction mapping principle to show error convergence. A quantized data-driven adaptive point-to-point ILC (QDDAPTPILC) is further presented using partial quantized measurements at the specified instants for multi-intermediate-point tracking. Simulation examples verify theoretical results and illustrate that the QDDAPTPILC outperforms the QDDAILC for multi-intermediate-point tracking tasks because it removes the unnecessary constraints.

In this article, the problem of event-based adaptive fuzzy fixed-time tracking control for a class of uncertain nonlinear systems with unknown virtual control coefficients (UVCCs) is considered. The unknown nonlinear functions of the considered systems are approximated by fuzzy-logic systems (FLSs). Moreover, a novel Lyapunov function is designed to remove the requirement of lower bounds of the UVCC in control laws. In addition, an event-triggered control method is developed by using the backstepping technique to save the network resources. Through theoretical analysis, the event-based fixed-time controller was proposed, which can guarantee that all signals of the controlled system are bounded and the tracking error can converge to a small neighborhood of the origin in a fixed time. Meanwhile, the convergence time is independent of the initial states. Two numerical examples are presented to demonstrate the effectiveness of the proposed approach.

In this article, a cooperative adaptive iterative learning fault-tolerant control (CAILFTC) algorithm with the radial basis function neural network (RBFNN) is proposed for multiple subway trains subject to the time-iteration-dependent actuator faults by using the multiple-point-mass dynamics model. First, an RBFNN is utilized to cope with the unknown nonlinearity of the subway train system. Next, a composite energy function (CEF) technique is applied to obtain the convergence property of the presented CAILFTC, which can guarantee that all train speed tracking errors are asymptotic convergence along the iteration axis; meanwhile, the headway distances of neighboring subway trains are kept in a safety range. Finally, the effectiveness of theoretical studies is verified through a subway train simulation.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

This article presents an event-triggered data-driven load frequency control (LFC) method for multiarea interconnected power systems via model-free adaptive control, where the dynamic model of the power system is assumed to be unknown completely. By introducing the dynamic linearization technique for the unknown power system, an equivalent data relationship model between the area-control-error (ACE) data and the input signal is established. Then, a data-driven LFC scheme is developed only relying on the input and output data of the power system. Meanwhile, an event-triggered strategy is also proposed in the design of data-driven LFC such that the communication and computation burden of the system can be reduced. Whether the current instant is the transmission instant is determined by judging the proposed triggering condition at each sampling instant. It is showed that the presented event-triggered data-driven LFC method is independent to any model information of the power system and does not need to measure any state signals. Simulation tests are carried out to verify the effectiveness of the presented control method.

Perimeter control (PC) and route guidance (RG) have become two powerful traffic control methods to address the urban traffic congestion, especially for multi-region urban traffic systems (MRUTS). Accurate traffic system model is necessary in majority of the existing PC and RG methods. If the traffic model is inaccurate or unavailable, the aforementioned PC and RG strategies may not work well or cannot be applied. In this paper, a novel data driven scheme called constrained model free adaptive predictive control (cMFAPC) is provided for PC and RG of MRUTS. Two outstanding advantages of this method are that it can only use the input and output (I/O) data of the controlled MRUTS to design the PC and RG strategies, instead of utilizing the traffic dynamics model, and the merits of model free adaptive control (MFAC) method and model predictive control (MPC) approach are combined in the proposed cMFAPC strategy. The effectiveness of cMFAPC strategy and its superiority over other commonly used PC and RG methods are verified via simulation.

This paper proposes a constrain spatial adaptive iterative learning controller (CSAILC) for the displacement-speed trajectory tracking of automatic train control system with unknown parametric/nonparametric uncertainties and speed constraints. First, the nonlinear dynamic model of train operation is transformed from temporal domain into spatial domain utilizing a spatial state differentiator. Besides, the displacement-related parametric/nonparametric uncertainties are updated in the iteration axis. Furthermore, a barrier function is involved to satisfy the speed constraint, and the corresponding convergence analysis of the proposed CSAILC for automatic train control (ATC) is derived based on the spatial composite energy function. In addition, numerical simulations of train tracking control are carried out, and simulation results indicate that the proposed CSAILC achieves good effectiveness in a high-speed train (HST) control system.

In this paper, a data-driven event-triggered cooperative control (DD-ETCC) scheme is proposed for the multiple subway trains to realize speed tracking and dynamic headway adjustment under switching topologies. Firstly, a nonlinear subway train system is transformed into a linearization data model, and the complex nonlinear terms caused by mechanical and aerodynamic resistance and operating environment conditions are estimated by projection algorithm. Then, the DD-ETCC scheme based on the linearization data model and the asynchronous event-triggered condition for multiple subway trains with switching topologies is designed. Theoretical analysis shows that the speed tracking errors of multiple subway trains are bounded, and the headway distances of consecutive trains are stabilized in a safe range with the proposed scheme. Finally, the effectiveness of the proposed DD-ETCC scheme of multiple trains is illustrated by subway train simulations.

This paper researches the cooperative control problem for multiple subway trains under the asynchronous data dropouts in both measurement channel and downlink channel. The compensation-based cooperative model free adaptive iterative learning control (cCMFAILC) for the multiple city subway trains (MCSTs) is proposed to avoid deterioration of the control performance due to data dropouts. First, the nonlinear subway train system is transformed into an equivalent dynamic linearization data model to describe the input-output dynamics of the subway train system. Next, the lost data is replaced by the corresponding data of the same time instant in the latest available iteration. And the cCMFAILC is designed to guarantee that the speed tracking errors of MCSTs are bounded along the iteration axis and the headway of neighboring subway trains is stabilized in a safe range. Finally, theoretical analysis and MCSTs simulations verify the validity of the proposed cCMFAILC scheme.

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach.

In this article, a model-free adaptive control (MFAC) algorithm based on full form dynamic linearization (FFDL) data model is presented for a class of unknown multi-input multi-output (MIMO) nonaffine nonlinear discrete-time learning systems. A virtual equivalent data model in the input-output sense to the considered plant is established first by using the FFDL technology. Then, using the obtained data model, a data-driven MFAC algorithm is designed merely using the inputs and outputs data of the closed-loop learning system. The theoretical analysis of the monotonic convergence of the tracking error dynamics, the bounded-input bounded-output (BIBO) stability, and the internal stability of the closed-loop learning system is rigorously proved by the contraction mapping principle. The effectiveness of the proposed control algorithm is verified by a simulation and a quad-rotor aircraft experimental system.

A data-driven distributed formation control algorithm is proposed for an unknown heterogeneous non-affine nonlinear discrete-time MIMO multi-agent system (MAS) with sensor fault. For the considered unknown MAS, the dynamic linearization technique in model-free adaptive control (MFAC) theory is used to transform the unknown MAS into an equivalent virtual dynamic linearization data model. Then using the virtual data model, the structure of the distributed model-free adaptive controller is constructed. For the incorrect signal measurements due to the sensor fault, the radial basis function neural network (RBFNN) is first trained for the MAS under the fault-free case, then using the outputs of the well-trained RBFNN and the actual outputs of MAS under sensor fault case, the estimation laws of the unknown fault and system parameters in the virtual data model are designed with only the measured input-output (I/O) data information. Finally, the boundedness of the formation error is analyzed by the contraction mapping method and mathematical induction method. The effectiveness of the proposed algorithm is illustrated by simulation examples.

Aiming to addressing the nonrepetitive uncertainties of multiagent systems, this work proposes a discrete-time-distributed adaptive iterative learning control (DDAILC) scheme for an output consensus problem, where two fundamental requirements in the traditional distributed iterative learning control (ILC) methods, i.e., the identical initial states and the repetitive desired trajectories, are removed. Furthermore, the algorithm design and analysis are directly aimed at discrete-time nonlinear multiagent systems, rather than continuous-time ones, to meet the needs of practical implementations. The iteration-varying trajectory of the virtual leader is included in the learning control protocol for a compensation. The adaptive parameter-updating law works along the iteration dimension by using a general consensus error that contains the output data of adjacent agents. To ensure the estimation of the control gain to be nonzero, a semisaturator is utilized in the parameter-updating law. The convergence of the output consensus is shown rigorously. Both numerical and practical examples are used to test the theoretical results. Moreover, the DDAILC efficiently improves performance of the building heating, ventilation, and air conditioning (HVAC) system by utilizing both the distributed topology and the repetitive dynamic characteristic.

In this article a novel data-driven iterative learning control (ILC) approach is proposed for unknown nonlinear nonaffine repetitive discrete-time systems, where the dynamic linearization (DL) technique in the iteration domain is applied both on the controlled nonlinear system and on the unknown nonlinear ideal learning controller. Through updating the weight matrix of a radial basis function neural network (RBFNN), the learning control gain of the obtained iterative learning law is automatically tuned in reaching the optimal learning controller using only the input-output data of the nonlinear system. The uniformly ultimately bounded property is established for the tracking error of the proposed ILC scheme in the iteration domain through rigorous theoretical analysis. The effectiveness and applicability are validated by a simulation example and further demonstrated by simulation on a high-speed train model.

This article studies the resilient control problem for a class of unknown nonlinear systems with fading measurements under malicious denial-of-service (DoS) attacks. The system output is assumed to be transmitted through a fading channel, where the fading phenomenon is described by a Rice fading model. The strategy of the attacker is to periodically interfere with the networked channels to reduce the success rate of data transmissions. First, a dynamic linearization method along the iteration domain is introduced to convert the nonlinear system into an equivalent data-related model. Then, a model-free adaptive iterative learning control (MFAILC) scheme is presented, which is independent of model information. The convergence of the MFAILC scheme is deduced theoretically and the influence of DoS attacks and stochastic fading phenomenon on system stability are also analyzed. Finally, the effectiveness of the design is verified by a numerical simulation and a trajectory tracking example of wheeled mobile robots (WMRs).

In this article, the tracking control problems of the nonlinear nonstrict-feedback systems are considered. By combining the backstepping technique and bound estimation method, a novel nonlinear adaptive asymptotical control law is proposed, which offsets the effect of the unknown virtual control parameters and the uncertain nonlinearities. Correspondingly, an improved Lyapunov function by introducing the lower bounds of control parameters has been devised in this article. Compared with the existing adaptive tracking control schemes, the controller designed in this article can guarantee that the tracking control error converges to zero asymptotically and all the signals which contain the state variables and the adaptive laws are bounded. Moreover, the asymptotic stability of the system is realized for the first time. Finally, simulation examples are applied to test and prove the availability of the presented methods and the performance of the controlled system.

This article proposed a novel adaptive ETC framework for asymptotic tracking of uncertain nonlinear systems in the presence of unknown virtual control coefficients (UVCC). More precisely, by introducing some well-defined smooth functions and the bounded estimation approach, the effects caused by the unknown UVCC and uncertainties are counteracted. Moreover, a novel Lyapunov function is constructed such that the asymptotical convergence to zero of the tracking error and boundedness of the closed-loop system are successfully achieved. Effectiveness of the proposed strategies is shown by using a simulation example.

In this article, a new adaptive fuzzy iterative learning control (AFILC) method is proposed for the tracking control of nonlinear uncertain high-speed train (HST) operation systems that have both randomly varying iteration lengths and speed and input force constraints. To cope with unknown time-varying basic resistance coefficients, an adaptive learning control law and two fully projected parameter learning laws are designed. The nonparametric and unknown additional resistance in the HST operation system is compensated and integrated into the control law by means of a newly constructed adaptive iterative learning fuzzy system. Moreover, due to the complex operation environment and various uncertainties, disturbances and emergencies, trains are often early or late compared with the prearranged timetable rather than being strictly on time in the repeated operations of each day, which leads to randomly varying operation lengths for actual HST running. Furthermore, as the traveling speed of modern HSTs increases, both the train's speed and input force should be constrained to guarantee the safe operation. Fortunately, the proposed AFILC can not only actively manipulate the position, speed, and input force of the train into prespecified and constrained ranges for safe operation but can also make both the position and speed tracking control errors converge to zero over the whole desired and scheduled time interval, even if the actual time interval varies in each operation of the HST. Simulations on a practical train operation system similar to China Railway High-speed (CRH)-3 train are further presented to demonstrate the applicability and effectiveness of the proposed method.

In urban traffic networks, abundant traffic data is generated everyday. Therefore, data-driven control approaches for urban traffic control without utilizing mathematical models might be a promising research direction. In this paper, a hierarchical perimeter control strategy for urban traffic networks based on model-free adaptive control (MFAC) scheme is proposed. At the outer level, the signal settings in the periphery of the congested region are optimized to meter the number of vehicles entering the congested region; while at the inner level, traffic flow distribution within the congested region is adjusted to improve the traffic efficiency. MFAC scheme is applied in both outer level and inner level to derive the detailed signal settings in the congested region and in the periphery of the congested region. Joint simulations using VISSIM and MATLAB verify the feasibility and effectiveness of the proposed method.

In this paper, a new adaptive iterative learning control method (AILC) is presented for speed and position tracking of a subway train using multiple-point-mass dynamic model. A composite energy function technique is utilized to obtain the asymptotic convergence of tracking error in the iteration axis for the proposed controller for subway trains. Then a speed constraint adaptive iterative learning control algorithm (CAILC) is designed to avoid over speed, derailment and collision of the subway train for the subway train over-speed protection. Finally, two simulation examples are given for the subway train system to show the effectiveness of theoretical studies.

This article considers the problem of finite-time consensus for nonlinear multiagent systems (MASs), where the nonlinear dynamics are completely unknown and the output saturation exists. First, the mapping relationship between the output of each agent at the terminal time and the control input is established along the iteration domain. By using the terminal iterative learning control method, two novel distributed data-driven consensus protocols are proposed depending on the input and output saturated data of agents and its neighbors. Then, the convergence conditions independent of agents' dynamics are developed for the MASs with fixed communication topology. It is shown that the proposed data-driven protocol can guarantee the system to achieve two different finite-time consensus objectives. Meanwhile, the design is also extended to the case of switching topologies. Finally, the effectiveness of the data-driven protocol is validated by a simulation example.

An event-triggered nonlinear iterative learning control (ET-NILC) method is presented for repetitive nonaffine and nonlinear systems that have 2-D dynamic behavior along both time and iteration directions. Based on the virtual linear data model, the ET-NILC method is proposed by designing an event triggering condition based on the Lyapunov-like stability analysis conducted along the iteration direction. The learning gain function of ET-NILC is nonlinear and updated by designing an iterative learning parameter estimation law to enhance the robustness. From the perspective of the time dynamics, the proposed ET-NILC is a feedforward control and the event-triggering condition can be verified offline using tracking errors, event triggering errors, and the estimated parameters together. Moreover, the proposed ET-NILC is a data-driven scheme since it merely uses I/O data for the design. The results are also extended to repetitive multiple-input-multiple-output (MIMO) nonaffine nonlinear systems using the property of input-to-state stability as the basic mathematical tool. The convergence of the proposed ET-NILC methods is proved. Several simulations illustrate the effectiveness of the proposed methods.

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

In this paper, an extended state observer-based data-driven iterative learning control [extended state observer (ESO)-based DDILC] is developed for a permanent magnet linear motor (PMLM). The PMLM is formulated mathematically by using a general nonlinear discrete-time system with consideration of exogenous disturbances. Then, a new iterative dynamic linearization (IDL) is proposed to equivalently reformulate the nonlinear PMLM system with a linear input-output incremental form involving iteration-varying initial states and disturbances. The concept of ESO is introduced into iteration direction to iteratively estimate the random initial states and disturbances as well as their corresponding partial derivatives by considering all of them as a whole extended state. The proposed ESO-based DDILC scheme contains a learning control algorithm and a gradient parameter updating algorithm obtained from two distinct objective functions, respectively. Moreover, the proposed method is data-driven and no explicit model is involved. Theoretical analysis shows the robustness of the proposed method in the presence of iteration-varying initial shifts and disturbances. The simulation on PMLM is conducted to confirm the validity and applicability of the ESO-based DDILC.

A sampled-data model-free adaptive control (SMFAC) strategy is proposed for continuous-time nonlinear nonaffine systems with input rate constraints. By using differential and integral mean value theorems as two basic mathematic tools, a sampled-data local dynamic linearization method is proposed at first to transform the continuous-time nonlinear nonaffine model into a sampled-data nonlinear affine I/O model, including a linear parametric term affined to the control input and a nonlinear uncertainty term. On this basis, we consequently propose an observer-based SMFAC (ObSMFAC) scheme, including a sampled-data parameter estimator to estimate the unknown partial derivatives and a sampled-data observer to estimate the residual nonlinear uncertainty, respectively. Note that the sampling period is incorporated explicitly in the proposed ObSMFAC which enhances the control performance by reducing its negative influence on the system stability. The constraint on the input rate is also considered in the control law as the transition condition of the input updating algorithms. The convergence of the proposed ObSMFAC is proved by using the contraction mapping principle. The simulation study demonstrates the theoretical results.

In this article, a radial basis function neural network-based adaptive iterative learning fault-tolerant control (RBFNN-AILFTC) algorithm is developed for subway trains subject to the time-iteration-dependent actuator faults and speed constraint by using the multiple-point-mass dynamic model. First, the RBFNN is utilized to approximate the time-iteration-dependent unknown nonlinearity of the subway train system; then, the iterative learning mechanism is used to tackle the outstanding repetitive operational pattern of a subway train which runs from one station to the next strictly according to the operation timetable schedule every day within the finite time interval, and the adaptive mechanism is designed for dealing with the time and the iteration-varying factors of the subway train. Second, a barrier composite energy function technique is exploited to obtain the convergence property of the proposed RBFNN-AILFTC scheme for subway train system, which can guarantee that the tracking error is asymptotic convergence along the iteration axis, meanwhile keep the speed profile of the subway train system satisfies the constraint. Finally, a subway train simulation is shown to verify the effectiveness of the theoretical studies.

The dynamical relationship of the multiple agents' behavior in a networked system is explored and utilized to enhance the control performance of the multiagent formation in this paper. An adjacent-agent dynamic linearization is first presented for nonlinear and nonaffine multiagent systems (MASs) and a virtual linear difference model is built between two adjacent agents communicating with each other. Considering causality, the agents are assigned as parent and child, respectively. Communication is from parent to child. Taking the advantage of the repetitive characteristics of a large class of MASs, an adjacent-agent dynamic linearization-based iterative learning formation control (ADL-ILFC) is proposed for the child agent using 3-D control knowledge from iterations, time instants, and the parent agent. The ADL-ILFC is a data-driven method and does not depend on a first-principle physical model but the virtual linear difference model. The validity of the proposed approach is demonstrated through rigorous analysis and extensive simulations.

Recent studies have shown that a homogenous urban road network exists a well-defined macroscopic fundamental diagram (MFD), which can be used for perimeter control conveniently. Most of the existing perimeter control strategies are model-based control methods, leading to the result that the control effect may be not good enough if the traffic model is not accurate. In this paper, a novel data-driven strategy called model free adaptive control (MFAC) method is proposed for multi-region perimeter control in order to get rid of the dependency of the aforementioned model-based MFD-based perimeter control methods. Due to the fact that the multi-region urban traffic system (MRUTS) is a complex interconnected system, a decentralized estimation and decentralized MFAC (DED-MFAC) method is utilized to deal with the strong-coupled characteristic of the traffic system. In this framework, MFD is used to determine the desired accumulations in each region and generate the throughput data of the urban traffic system, since the acquisition of trip completion flow is more difficult than accumulations. In addition, route choice is also integrated in the proposed policy to further improve the performance of the urban traffic system. A key advantage of the proposed approach is that it can only use the traffic data instead of the traffic model for real-time perimeter control. The effectiveness of the proposed perimeter control scheme is tested in simulation for a multi-region system, and the results show that it is superior to some other commonly used perimeter control methods.

This paper explores the formation control problem of repetitive nonlinear homogeneous and asynchronous multiagent networks, where the early starting agent is designated as the parent, and the later starting agent with a small delayed time is designated as the child. Moreover, the desired formation reference is allowed to be different from iteration to iteration. A space-dimensional dynamic linearization method is presented to build the linear dynamic relationship between two parent-child agents in a networked system. Then, a 3-D learning-enhanced adaptive iterative learning control (3D-AILC) is proposed by utilizing the additional control information from previous time instants, iterative operations, and parent agents. In other words, the proposed method processes 3-D dynamics to strengthen its learnability, i.e., time dimension, iteration dimension, and space dimension. The desired formation signal is incorporated into the learning control law to compensate its iterative variation to achieve a fast and precise tracking performance. The proposed 3D-AILC is data based and does not use an explicit mechanistic model. The validity of the proposed approach is proven theoretically and tested through simulations as well. Moreover, the proposed method also works well with time-iteration-varying topologies and nonrepetitive uncertainties.

In this paper, a novel data-driven predictive iterative learning control (DDPILC) scheme based on a radial basis function neural network (RBFNN) is proposed for a class of repeatable nonaffine nonlinear discrete-time systems subjected to nonrepetitive external disturbances. First, by utilizing the dynamic linearization technique (DLT) with a newly introduced and unknown system parameter pseudopartial derivative (PPD) and designing a new RBFNN estimation algorithm along the iterative learning axis for addressing the unknown PPD and the unknown nonrepetitive external disturbances, a data-driven prediction model is established. It is theoretically shown that by constructing a composite energy function (CEF) with respect to the modeling error for the first time, the convergence of the modeling error via the proposed DLT-based RBFNN modeling method can be guaranteed, and the convergence speed is tunable. Then, a DDPILC with a disturbance compensation term is designed, and the convergence of the tracking control error is analyzed. Finally, simulations of a train operation system reveal that even if the train suffers from randomly varying load disturbances and nonlinear running resistance, the proposed scheme can make both the modeling error and the tracking control error decrease successively with increasing operation number.

This paper considers the problem of data driven iterative learning control (DDILC) for a class of nonaffine nonlinear systems subject to data quantization and sensor saturation. Two novel quantized DDILC (QDDILC) algorithms are proposed based on saturated and quantized information of system outputs. The convergence of the proposed QDDILC algorithms is strictly proved and the effects of output saturation and data quantification are also analyzed. It is shown that sensor saturation does not change the convergence property, thus it causes the convergence rate to slow down. For the QDDILC algorithm, data quantization will cause the tracking error to converge to a bound depending on the quantization level. However, the modified QDDILC algorithm, which using the different quantization scheme from QDDILC algorithm, can ensure that the tracking error converges to zero. Illustrative simulations are exploited to verify the theoretical results.

Fast and efficient evacuation of pedestrians from an enclosed area is a difficult but crucial issue in modern society. In this paper, the optimization of evacuation from a building is studied. A graph is adopted to describe the building layout with nodes representing areas and edges representing connections. The dynamics of the evacuation process in the graph is formulated by a nonlinear discrete-time model at a macroscopic level. To find the optimal evacuation plan, a consecutive differential dynamic programming is developed. It inherits the differential dynamic programming property that solves the value and optimal policy locally. Additionally, it consecutively executes actions for multiple steps in the trajectory, which is beneficial to reduce computational burden and lower optimization difficulty. Simulations on a four-storey building layout demonstrates our method is efficient and suitable for on-site evacuation plan making.

In this paper, a novel model-free adaptive control (MFAC) algorithm based on a dual successive projection (DuSP)-MFAC method is proposed, and it is analyzed using the introduced DuSP method and the symmetrically similar structures of the controller and its parameter estimator of MFAC. Then, the proposed DuSP-MFAC scheme is successfully implemented in an autonomous car "Ruilong" for the lateral tracking control problem via converting the trajectory tracking problem into a stabilization problem by using the proposed preview-deviation-yaw angle. This MFAC-based lateral tracking control method was tested and demonstrated satisfactory performance on real roads in Fengtai, Beijing, China, and through successful participation in the Chinese Smart Car Future Challenge Competition held in 2015 and 2016.

This paper proposes a distributed model free adaptive iterative learning control (MFAILC) method for a class of unknown nonlinear multiagent systems to perform consensus tracking. Here, both fixed and iteration-varying topologies are considered and only a subset of followers can access the desired trajectory in each topology. To design the control protocol, the agent’s dynamic is first transformed into a dynamic linearization model along the iteration axis, and then a distributed MFAILC scheme is constructed to guarantee that all agents can track the desired trajectory. Through rigorous analysis, it is shown that under this novel distributed MFAILC scheme, the tracking errors of all agents are convergent along the iteration axis. The main merit of this design is that consensus tracking task can be achieved only utilizing the input/output data of the multiagent system. Three examples are given to validate the effectiveness of the proposed design.

In this paper, an improved data-driven point-to-point iterative learning control is proposed for nonlinear repetitive systems where only the system outputs at the multiple intermediate prespecified points are considered. The entire finite time interval is divided into multiple time-subintervals according to the prespecified points. Then a new objective function is designed to generate optimal control inputs over a time-subinterval piecewisely. As a result, the control inputs are updated in a time-subinterval wise using additional input signals from the previous time-subintervals of the same iteration to help improving control performance. By removing the constraints on the unimportant intermediate points, the control system can be designed with additional freedom to achieve a better performance in tracking points of interest. Meanwhile, the proposed approach is data-driven and no process model is required for the control system design and analysis. Both a simulation with nonlinear batch reactor and an experiment with a permanent magnet linear motor servomechanism are provided to demonstrate the effectiveness of the proposed method.

This brief presents a novel adaptive iterative learning control (ILC) algorithm for a class of single parameter systems with binary-valued observations. Using the certainty equivalence principle, the adaptive ILC algorithm is designed by employing a projection identification algorithm along the iteration axis. It is shown that, even though the available system information is very limited and the desired trajectory is iteration-varying, the proposed adaptive ILC algorithm can guarantee the convergence of parameter estimation over a finite-time interval along the iterative axis; meanwhile, the tracking error is pointwise convergence asymptotically. Two examples are given to validate the effectiveness of the algorithm.

This paper investigates the data-driven consensus tracking problem for multiagent systems with both fixed communication topology and switching topology by utilizing a distributed model free adaptive control (MFAC) method. Here, agent's dynamics are described by unknown nonlinear systems and only a subset of followers can access the desired trajectory. The dynamical linearization technique is applied to each agent based on the pseudo partial derivative, and then, a distributed MFAC algorithm is proposed to ensure that all agents can track the desired trajectory. It is shown that the consensus error can be reduced for both time invariable and time varying desired trajectories. The main feature of this design is that consensus tracking can be achieved using only input-output data of each agent. The effectiveness of the proposed design is verified by simulation examples.

Based on a nonlifted iterative dynamic linearization formulation, a novel data-driven higher order optimal iterative learning control (DDHOILC) is proposed for a class of nonlinear repetitive discrete-time systems. By using the historical data, additional tracking errors and control inputs in previous iterations are used to enhance the online control performance. From the online data, additional control inputs of previous time instants within the current iteration are utilized to improve transient response. The data-driven property of the proposed method implies that no model information except for the I/O data is utilized. The computational complexity is reduced by avoiding matrix inverse operation in the proposed DDHOILC approach due to the nonlifted linear formulation of the original model. The asymptotic convergence is proved rigorously. Furthermore, the convergence property is analyzed and evaluated via three performance indexes. By elaborately selecting the higher order factors, the higher order learning control law outperforms the lower order one in terms of convergence performance. Simulation results verify the effectiveness of the proposed approach.

In this paper, a novel data-driven model-free adaptive predictive control method based on lazy learning technique is proposed for a class of discrete-time single-input and single-output nonlinear systems. The feature of the proposed approach is that the controller is designed only using the input-output (I/O) measurement data of the system by means of a novel dynamic linearization technique with a new concept termed pseudogradient (PG). Moreover, the predictive function is implemented in the controller using a lazy-learning (LL)-based PG predictive algorithm, such that the controller not only shows good robustness but also can realize the effect of model-free adaptive prediction for the sudden change of the desired signal. Further, since the LL technique has the characteristic of database queries, both the online and offline I/O measurement data are fully and simultaneously utilized to real-time adjust the controller parameters during the control process. Moreover, the stability of the proposed method is guaranteed by rigorous mathematical analysis. Meanwhile, the numerical simulations and the laboratory experiments implemented on a practical three-tank water level control system both verify the effectiveness of the proposed approach.

In this brief, we propose a new data-driven model-free adaptive control (MFAC) method with dual radial basis function neural networks (RBFNNs) for a class of discrete-time nonlinear systems. The main novelty lies in that it provides a systematic design method for controller structure by the direct usage of I/O data, rather than using the first-principle model or offline identified plant model. The controller structure is determined by equivalent-dynamic-linearization representation of the ideal nonlinear controller, and the controller parameters are tuned by the pseudogradient information extracted from the I/O data of the plant, which can deal with the unknown nonlinear system. The stability of the closed-loop control system and the stability of the training process for RBFNNs are guaranteed by rigorous theoretical analysis. Meanwhile, the effectiveness and the applicability of the proposed method are further demonstrated by the numerical example and Aspen HYSYS simulation of distillation column in crude styrene produce process.

Macroscopic fundamental diagram (MFD) that describes traffic flow in an urban road network can be used to design perimeter control method to regulate the traffic flow from a macroscopic level. Most of the perimeter control algorithms are regarded as a kind of model-based feedback control method, whose performance is hardly to improve in practice due to the model uncertainty. By noticing the repetitive nature of urban traffic flow, an iterative learning control (ILC) based perimeter control method is proposed for an urban region. Since the repetitive information of the controlled system is fully utilized, an improved tracking performance is guaranteed by theoretical analysis, and simulation results verify the effectiveness of the proposed perimeter control method.

In this work, a novel model free adaptive control method based on a mathematical algorithm named double successive projection (DSP-MFAC) is proposed, from which it can be inferred that conventional MFAC algorithm is only a special case of DSP-MFAC with the Cartesian product of the output and the input Hilbert space. For a general unknown nonlinear system, an innovative partial form dynamic linearization (PFDL) technique is first presented based on a new concept named pseudo gradient (PG). Then, the controller for the system is designed based on the PG with the aid of a novel DSP algorithm modified from the conventional successive projection algorithm. Consequently, the structures of the controller and its parameters estimator are symmetric similar, which makes the control performance become stable. Meanwhile, the convergence of DSP-MFAC for a regulation problem of a class of nonlinear discrete systems are guaranteed by rigorous mathematical analysis under several reasonable assumptions. Furthermore, numerical simulation results show that DSP-MFAC is effective and applicable.

In this paper, an adaptive iterative learning control (AILC) strategy for high-speed trains with unknown speed delays and control input saturations is designed to address speed trajectory tracking problem. The train motion dynamics containing nonlinearities and parametric uncertainties are formulated as a nonlinearly parameterized system. Instead of estimation or modeling of train delays, an unknown time-varying delay term is integrated into the speed on delay analysis by means of Lyapunov-Krasovskii function. Through rigorous analysis, it is confirmed that the proposed AILC mechanism can guarantee L[0, T]2convergence of train speed to the desired profile during operations repeatedly. Case studies with numerical simulations further verify the effectiveness of the proposed approach.

In this paper, by splitting a traffic flow series into basis series and deviation series, the concepts of similarity and repeatability of traffic flow patterns are defined using the statistic average values of the basis series and the deviation series and are further verified through the real-time big traffic data of 82 days with a sampling period of 5 min collected from two typical ones among a total of 102 detecting sites in Shenzhen, China. Meanwhile, based on the repeatability and the similarity of the traffic flow series, a novel long-term forecasting method for traffic flow is developed, and hybrid forecasting algorithms for short-/long-term traffic flow prediction are also proposed. The effectiveness of these algorithms is verified by using the real-time data.

In this brief, an enhanced genetic back-propagation neural network with link switches (EGA-BPNN-LS) is proposed to address a data-driven modeling problem for gasification processes inside United Gas Improvement (UGI) gasifiers. The online-measured temperature of crude gas produced during the gasification processes plays a dominant role in the syngas industry; however, it is difficult to model temperature dynamics via first principles due to the practical complexity of the gasification process, especially as reflected by severe changes in the gas temperature resulting from infrequent manipulations of the gasifier in practice. The proposed data-driven modeling approach, EGA-BPNN-LS, incorporates an NN-LS, an EGA, and the Levenberg-Marquardt (LM) algorithm. The approach cannot only learn the relationships between the control input and the system output from historical data using an optimized network structure through a combination of EGA and NN-LS but also makes use of the networks gradient information via the LM algorithm. EGA-BPNN-LS is applied to a set of data collected from the field to model the UGI gasification processes, and the effectiveness of EGA-BPNN-LS is verified.

In this paper, an enhanced data-driven optimal terminal iterative learning control (E-DDOTILC) is proposed for a class of nonlinear and nonaffine discrete-time systems. A dynamical linearization approach is first developed with iterative operation points to formulate the relationship of system output and input into a linear affine form. Then, an ILC law is constructed with a nonlinear learning gain, which is a function about the system partial derivative with respect to the time-varying control input. In addition, a parameter updating law is designed to estimate the unknown partial derivatives iteratively. The input signals of the proposed E-DDOTILC are time-varying and updated utilizing not only the terminal tracking error of the previous run but also the input signals of the previous time instants in the current iteration. The proposed approach is a data-driven control strategy and only the I/O data are required for the controller design and analysis. The monotonic convergence and effectiveness of the proposed approach is further verified by both the rigorous mathematical analysis and the simulation results.

An enhanced genetic BP neural network with link switches (EGA-VRBPNN) is proposed in this work to address the data-driven modeling problem for the gasification process inside a UGI gasifier. During gasification processes, the online measured gas temperature is crucial but difficult to model its' dynamics via first principles because of the tremendous complexity of the gasification process, which is mainly reflected from severe changes of the gas temperature versus infrequent and small manipulations of parts of the input variables. EGA-VRBPNN, which incorporates a neural networks with link switches (NN-LS) with an enhanced genetic algorithm (EGA) and the Levenberg-Marquardt (LM) algorithm, can not only learn the relationships between control inputs and system outputs from historical data with the help of optimized network structure through combination of the EGA and NN-LS, but also overcome the drawbacks of gradient-based method and make full use of the network's gradient information to achieve a satisfactory accuracy. A set of data collected from the practical fields are applied to modeling via the EGA-VRBPNN, by which the effectiveness of the EGA-VRBPNN is verified.

This work embodies the overspeed protection and safe headway control into an iterative learning control (ILC) based train trajectory tracking algorithm to satisfy the high safety requirement of high-speed railways. First, a D-type ILC scheme with overspeed protection is proposed. Then, a corresponding coordinated ILC scheme with multiple trains is studied to keep the safe headway. Finally, the control scheme under traction/braking force constraint is also considered for this proposed ILC-based train trajectory tracking strategy. Rigorous theoretical analysis has shown that the proposed control schemes can guarantee the asymptotic convergence of train speed and position to its desired profiles without requirement of the physical model aside from some mild assumptions on the system. Effectiveness is further evaluated through simulations.

In this work, a new iterative feedback tuning approach is proposed to tune ALINEA's controller gain automatically when there is not enough prior information available to select a proper feedback gain of ALINEA. It is a data-driven method and the ALINEA controller is auto-tuned only depending on the input and output data collected from closed-loop experiments. To mimic a real traffic environment, a simulator is built on the PARAMICS platform. The flow-based ALINEA controller is also considered to illustrate the good tuning performance of IFT comprehensively. The effectiveness of the proposed methods is verified through PARAMICS based simulations.

A new type of model free adaptive control (MFAC) method, including MFAC scheme designs with the compact-form-dynamic-linearization-based controller (CFDLc) and partial-form-dynamic-linearization-based controller (PFDLc), is presented for a class of discrete-time SISO nonlinear systems. The proposed method is a pure data-driven control method since the controller is independent of the model of the controlled plant, and controller parameter tuning is merely based on the measured I/O data of the controlled plant in closed loop. Differing from the MFAC prototype, the proposed method uses the dynamic linearization approach not only on ideal controller but also on the plant. The stability of the CFDLc-MFAC and PFDLc-MFAC is guaranteed by rigorous theoretical analysis, and the effectiveness is evaluated on simulation examples and a three-tank liquid control experimental system.

In the past decade, adaptive critic designs (ACDs), including heuristic dynamic programming (HDP), dual heuristic programming (DHP), and their action-dependent ones, have been widely studied to realize online learning control of dynamical systems. However, because neural networks with manually designed features are commonly used to deal with continuous state and action spaces, the generalization capability and learning efficiency of previous ACDs still need to be improved. In this paper, a novel framework of ACDs with sparse kernel machines is presented by integrating kernel methods into the critic of ACDs. To improve the generalization capability as well as the computational efficiency of kernel machines, a sparsification method based on the approximately linear dependence analysis is used. Using the sparse kernel machines, two kernel-based ACD algorithms, that is, kernel HDP (KHDP) and kernel DHP (KDHP), are proposed and their performance is analyzed both theoretically and empirically. Because of the representation learning and generalization capability of sparse kernel machines, KHDP and KDHP can obtain much better performance than previous HDP and DHP with manually designed neural networks. Simulation and experimental results of two nonlinear control problems, that is, a continuous-action inverted pendulum problem and a ball and plate control problem, demonstrate the effectiveness of the proposed kernel ACD methods.

Most of the available results of adaptive iterative learning control (AILC) hitherto have considered the control systems with known linearly parameterized structures. A dynamical linearization approach is developed for a general nonlinear multiple input multiple output systems. And then a discrete-time adaptive ILC approach is presented to deal with the ILC problems of nonlinear MIMO systems with iteration-varying initial error and reference trajectory. The controller design and analysis is completely data-driven without using any modeling information of the plant, but the measured I/O data only. The almost perfect tracking performance is asymptotically guaranteed by rigirous mathematical analysis.

For a freeway traffic system with strict repeatable pattern, iterative learning control (ILC) has been successfully applied to local ramp metering for a macroscopic freeway environment by formulating the original ramp metering problem as an output tracking, disturbance rejection, and error compensation problem. In this paper, we address the freeway traffic ramp-metering system under a nonstrict repeatable pattern. ILC-based ramp metering and ILC add-on to ALINEA strategies are modified to deal with the presence of iteration-dependent parameters, iteration-dependent desired trajectory, and input constraints. Theoretical analysis and extensive simulations are used to verify the effectiveness of the proposed approaches.

Ramp metering is an effective tool for traffic management on freeway networks. In this paper, we apply iterative learning control (ILC) to address ramp metering in a macroscopic-level freeway environment. By formulating the original ramp metering problem as an output regulating and disturbance rejection problem, ILC has been applied to control the traffic response. The learning mechanism is further combined with Asservissement Linéaire d'Entrée Autoroutière (ALINEA) in a complementary manner to achieve the desired control performance. The ILC-based ramp metering strategy and the modified modularized ramp metering approach based on ILC and ALINEA in the presence of input constraints are also analyzed to highlight the advantages and the robustness of the proposed methods. Extensive simulations are given to verify the effectiveness of the proposed approaches.

The 21 papers in this special section focus on data-based control, modeling, and optimization.

In this paper, a data-driven model-free adaptive control (MFAC) approach is proposed based on a new dynamic linearization technique (DLT) with a novel concept called pseudo-partial derivative for a class of general multiple-input and multiple-output nonlinear discrete-time systems. The DLT includes compact form dynamic linearization, partial form dynamic linearization, and full form dynamic linearization. The main feature of the approach is that the controller design depends only on the measured input/output data of the controlled plant. Analysis and extensive simulations have shown that MFAC guarantees the bounded-input bounded-output stability and the tracking error convergence.

Iterative learning control (ILC) is considered for both deterministic and stochastic systems with unknown control direction. To deal with the unknown control direction, a novel switching mechanism, based only on available system tracking error data, is first proposed. Then two ILC algorithms combined with the novel switching mechanism are designed for both deterministic and stochastic systems. It is proved that the ILC algorithms would switch to the right control direction and stick to it after a finite number of cycles. Moreover, the input sequence converges to the desired one under the deterministic case. The input sequence converges to the optimal one with probability 1 under stochastic case and the resulting tracking error tends to its minimal value.