This paper studies an iterative learning-based adaptive containment control for a kind of repetitive multiagent systems (MASs) with a nonstrict-feedback structure. The hyperbolic tangent function and the mean value theory are combined to handle the input saturation problem. Then, we establish a relationship between the original system state and compromised system state to resolve the impact of the false data injection (FDI) attack on the system performance. Under the framework of backstepping, the nonstrict-feedback issue is addressed by using the property of the fuzzy logic system. However, it is inevitable to generate two unknown control gains during the process of addressing the input saturation and FDI attack. As a result, an estimated scheme is proposed to approximate their bound. Moreover, two auxiliary functions are introduced to the virtual controller to reduce the influence of the sign function, and achieve the asymptotic convergence. The proposed scheme guarantees that all the followers converge to a convex hull spanned by the leaders as the iteration approaches infinity. Finally, two simulation examples are considered to verify the effectiveness of the designed method.

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.

This work investigates the consensus learning control for heterogeneous nonlinear multiagent systems (MASs) under false data injection (FDI) attacks on the communication channels. An enhanced iterative dynamic linearization (EiDL) method is introduced to transform the nonlinear MAS into an equivalent linearization data model, where additional parameters are used to reflect the uncertainties of the MAS. Assume that the communication among agents is subject to a stochastic FDI attack which is modeled by a weighted sum of attacks for adjacent communication channels. Then, combining the event-triggering condition along the iterative direction, an event-triggered data-driven iterative learning control (ET-DDILC) is proposed where the attacked information is used in control law and parameter estimation law to counteract the impact of FDI attacks. The convergence is proven by introducing additional tools of mathematical expectations and matrix theory. Moreover, the proposed ET-DDILC is further extended to the MASs under iteration-switching topologies. Extensive simulation results verify that the proposed ET-DDILC can achieve a good control performance against injection attacks without using any model information while simultaneously saving system resources through the event-triggering mechanism.

This work studies Denial-of-Service (DoS) attacks for strongly connected nonaffine nonlinear multi-agent systems (MASs). At first, we develop a network topology-based linear data model (NT-LDM) to reformulate the input/output behavior among the agents. A dynamic consensus protocol is derived using the NT-LDM to enhance the consensus performance of the network topology. Meanwhile, a combined attack compensation mechanism, incorporating both input and output, is introduced for reducing the poor influence of DoS attacks on network communication. Then, an input-behavior-learning-based data-driven control (IBL-DDC) is developed to improve the consensus protocol by designing an attack compensation scheme to the unavailable data due to DoS attacks. The proposed IBL-DDC not only is independent on the system model, but also can reject DoS attacks by learning from the input action of other agents through the proposed compensation scheme. The results are confirmed by the simulation study.

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.

Considering the four challenges of non-identical initial states, non-repetitive uncertainties, different batch lengths, and unavailable mathematical model of a rubber mixing process (RMP), this article proposes a data-driven iterative learning temperature control (DDILTC) for the RMP. Specifically, an iterative linear data model (iLDM) is developed to formulate the iterative dynamics of RMP and is further used as a one-step iterative linear predictive model to estimate the RMP’s temperature that is unavailable when the current batch length is shorter than the desired one. The unknown parameters of the iLDM are estimated iteratively by designing an iterative adaption law. Further, an iterative learning based observer is designed to estimate the non-repetitive uncertainties and non-identical initial states as an extended state. The proposed DDILTC is a data-driven method and the iLDM is only used to formulate the iterative relationship of the input-output between two batches instead of a mathematical model of the RMP with physical meanings. Simulation study verifies the results. Note to Practitioners—The mixing temperature of a rubber mixing process (RMP) is a critical variable, ensuring the desired plasticity and viscosity of the rubber compounds. Indeed, RMP is a typical batch process performing repetitively over the finite time interval. However, no ILC results about the RMP temperature control have been reported even though ILC can learn the control experience from the past batches to improve control performance. The main reason lies in that the practical environments of RMP make it impossible to satisfy the strictly repetitive conditions, i.e., the initial states, disturbances, and batch lengths are all iteration-varying. Furthermore, it is difficult to establish a mathematical model of the RMP due to its large production scale and complex dynamics along both time and iteration directions. Therefore, the main motivation of this paper is to study the iterative learning temperature control problem of RMP by considering the nonrepetitive uncertainties of initial states, disturbances, and batch lengths, bypassing the use of any model information. An iterative linear data model (iLDM) is established to equivalently reformulate the unavailable two-dimensional dynamic behavior of RMP and to facilitate the controller design and analysis. The gradient uncertainty of RMP is reformulated as the unknown parameters in the iLDM and can be iteratively estimated by designing an iterative adaptation algorithm. The non-repetitive initial states and disturbances can be estimated by designing an iterative observer. Moreover, the unavailable mixing temperatures at the unreachable operation points are estimated by using the iLDM as the iterative predictive model. To summarize, the proposed method is simple in computation and easy in implementation since only the I/O data is used, and thus it is of great practical significance.

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.

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.

A novel data-driven internal model learning control (DIMLC) strategy is developed for a nonlinear nonaffine system subject to unknown nonrepetitive uncertainties. At first, an iterative dynamic linearization (IDL) approach is employed for reformulating the nonlinear plant to an iterative linear data model (iLDM). Then, the nominal form of the IDL-based iLDM is used as an internal model of the nonlinear plant whose parameters are estimated by an iterative adaptive updating mechanism using only input-output (I/O) data. The equivalent feedback-principle-based internal model inversion is further applied to the subsequent controller design and analysis. The proposed DIMLC contains two parts. One is a nominal controller designed by the inversion of the internal model which achieves a perfect tracking of the target output; the other is a compensatory controller which offsets the uncertainties. The novel DIMLC is data-driven and does not require an explicit model. It can deal with model-plant mismatch and disturbances, enhancing the robustness against uncertainties. The theoretical results are verified by simulation study.

Aiming to solve issues of limited resources in topology network communication, unavailability of the mathematical models, direct controller design without considering system dynamical formulation, and lack of efficient use of learning ability from repetitive operations, an event-triggered direct data driven iterative learning control (ET-DirDDILC) is developed for a multiagent system (MAS). Since the control protocol directly affects control performance, there is definitely a close relationship between the consensus performance of the agents and the control protocols. To this end, a nonaffine nonlinear relationship of consensus error regarding the control protocol is established. Then, to deal with the unknown nonlinearity, a dynamic linear input–output relationship between two triggered batches is established by an event-triggering linearly parametric data model (ET-LPDM) where a triggering mechanism is designed along the iteration axis. Furthermore, both the event-triggered control law and the event-triggered parameter estimation law are derived from two objective functions, respectively, by using the ET-LPDM, where the values at nontriggering iteration remain unchanged from the latest triggering iteration to reduce the consumption of system resources. The proposed ET-DirDDILC does not rely on the MAS dynamical formulation. The convergence is proved and simulation study verifies the effectiveness of the presented ET-DirDDILC for MASs with both fixed and switching topologies.

Differential privacy preserving ensures the privacy of the system data by adding certain regular noises to the data to cover up the real information. The main challenges of strong nonlinearities, uncertainty, and data privacy are considered together for switched systems, and a novel privacy-preserving robust model-free adaptive predictive control (PPR-MFAPC) method is proposed that guarantees both$H_{\infty }$performance and system privacy. At first, a performance-dependent differential privacy noise conforming the Laplace distribution is designed, which can adaptively adjust the noise size to balance the system performance and privacy. Then, a novel privacy level analysis with evaluation method is presented. Subsequently, the strong uncertainties of switched systems is solved through a dynamic linearization method. On this basis, a novel cost function is designed by considering both the$H_{\infty }$performance and system privacy to balance the system performance and privacy from the perspective of control design. Further, by incorporating a parameter estimator and a prediction algorithm, the private MFAPC anti-noise controller is obtained. Finally, the feasibility of the PPR-MFAPC is explained with illustrative example.

This article investigates the control problem for a sort of repetitive discrete-time nonlinear systems subject to random packet dropouts and limited communication bandwidth. In order to compensate the impacts from the constraints on bandwidth, this work designs a communication protocol by designing a two-description coding scheme in combination with the scalar uniform quantization technique. The proposed protocol makes use of two independent channels to transmit data separately, thereby improving the channel utilization efficiency and reducing the probability of packet dropout. Then, with the proposed protocol and the iterative dynamic linearization approach, an adaptive iterative learning controller associated with a parameter estimation strategy is provided for the nonlinear system under investigation. The control law is data-driven, which therefore does not require knowledge of the model. Subsequently, the sufficient condition is derived under which the tracking error is forced to convergent. Finally, with the purpose to show the correctness of our theoretical results, we carry out two numerical simulations to test the effectiveness of the proposed control strategy.

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.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

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.

This work considers three main problems related to fast finite-iteration convergence (FIC), nonrepetitive uncertainty, and data-driven design. A data-driven robust finite-iteration learning control (DDRFILC) is proposed for a multiple-input-multiple-output (MIMO) nonrepetitive uncertain system. The proposed learning control has a tunable learning gain computed through the solution of a set of linear matrix inequalities (LMIs). It warrants a bounded convergence within the predesignated finite iterations. In the proposed DDRFILC, not only can the tracking error bound be determined in advance but also the convergence iteration number can be designated beforehand. To deal with nonrepetitive uncertainty, the MIMO uncertain system is reformulated as an iterative incremental linear model by defining a pseudo partitioned Jacobian matrix (PPJM), which is estimated iteratively by using a projection algorithm. Further, both the PPJM estimation and its estimation error bound are included in the LMIs to restrain their effects on the control performance. The proposed DDRFILC can guarantee both the iterative asymptotic convergence with increasing iterations and the FIC within the prespecified iteration number. Simulation results verify the proposed algorithm.

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.

In the realm of data-driven adaptive iterative learning control (AILC), the emphasis in designing and analyzing control schemes mainly concentrates on discrete-time systems, while fewer results are developed for the more common continuous-time plants. To overcome this limitation, a practical sampled-data AILC (SDAILC) is developed for continuous-time nonaffine nonlinear plants. A sampled-data iterative dynamic linearization (SDIDL) method is devised to build the dynamic connection between input and output (I/O) data throughout different iterations. On this basis, the SDAILC method, including a sampled-data parameter estimation algorithm and a learning control law, is proposed by utilizing optimization-based design. In SDAILC, the sampling period is treated as a parameter to compensate for its influence on the control performance, and an error feedback is naturally involved, improving the robustness against uncertainties and the closed-loop stability of the plant. Notably, SDAILC is a data-driven approach independent of model information. The validity of SDAILC is proved mathematically and demonstrated by simulations.

This work aims at improving the control performance of the iterative learning control through set-point learning along iteration direction. A double-layered learning control mechanism is designed for both the control input and the set-point, respectively. The learning control of the input is regarded as a local controller in the inner layer, and the learning control of the set-point is designed as an auxiliary controller in the outer layer whose design is a main challenge since no any priori knowledge is available to describe the relationship between the set-point and the control performance. To solve this issue, an ideal nonlinear nonaffine set-point learning optimization (SPLO) algorithm is designed by taking the set-point and the tracking error as the arguments. Then, an iterative dynamic linearization (iDL) is introduced to formulate the ideal SPLO algorithm as a linear parametric one whose unknown parameter is estimated by designing a parameter updating algorithm. Further, since a strongly nonlinear and nonaffine system is considered without any model information available, the iDL is also used to derive its equivalent linear data model which is then updated by the input and output data to make the linear parametric SPLO realizable. Finally, a double-layered iterative learning control (DLILC) is proposed under the data-driven framework for tracking an iteration-varying trajectory. Convergence analysis and extensive simulations are included to demonstrate the effectiveness of the presented DLILC.

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.

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.

This article aims at solving the problems of data-driven control design in the presence of strong uncertainties, hard nonlinearities, and model dependency by using a dynamic linearization (DL) method and an extended state observer (ESO). An unknown nonlinear nonaffine system is considered, whose input–output dynamics is then equivalently reformulated into a modified linear data model (mLDM) in which both a linear parametric increment description that is affine to the control input and the unmodeled uncertainties along with disturbances are included without omission or approximation. The uncertain parameter of the mLDM is estimated in real time by designing an adaptive mechanism, and the unmodeled uncertainties and disturbances are considered as a total extended state which is further estimated by developing a linear ESO. Subsequently, a modified DL-and-ESO-based data-driven adaptive control (mDLESO-DDAC) is proposed by using knowledge from previous control input to improve the control performance. The theoretical results are mathematically proved and then verified by 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.

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 optimal consensus problem at specified data points is considered for heterogeneous networked agents with iteration-switching topologies. A point-to-point linear data model (PTP-LDM) is proposed for heterogeneous agents to establish an iterative input-output relationship of the agents at the specified data points between two consecutive iterations. The proposed PTP-LDM is only used to facilitate the subsequent controller design and analysis. In the sequel, an iterative identification algorithm is presented to estimate the unknown parameters in the PTP-LDM. Next, an event-triggered point-to-point iterative learning control (ET-PTPILC) is proposed to achieve an optimal consensus of heterogeneous networked agents with switching topology. A Lyapunov function is designed to attain the event-triggering condition where only the control information at the specified data points is available. The controller is updated in a batch wise only when the event-triggering condition is satisfied, thus saving significant communication resources and reducing the number of the actuator updates. The convergence is proved mathematically. In addition, the results are also extended from linear discrete-time systems to nonlinear nonaffine discrete-time systems. The validity of the presented ET-PTPILC method is demonstrated through simulation studies.

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.

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.

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.

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.

This paper investigates an event-triggered model-free adaptive control for nonaffined nonlinear systems under a data-driven design framework. By introducing a compact form dynamic linearization (CFDL) scheme, a linear data model of the nonlinear nonaffine system is derived. Then, a parameter estimation algorithm is developed to offline identify the linear data model. On the basis of the identified linear data model, a CFDL-based event-triggered model-free adaptive control (CFDL-ET-MFAC) is developed by designing an event-triggering condition to guarantee the Lyapunov stability. The control action is active only when the event-triggering condition is satisfied. Otherwise, the input signal remains the same as that at the previous triggering instant. In addition, the parameter estimation algorithm is developed for the proposed CFDL-ET-MFAC to identify the CFDL model in real time for improving the robustness to the uncertainties. Meanwhile, both a partial form dynamic linearization-based event-triggered MFAC and a full form dynamic linearization-based event-triggered MFAC are proposed to further improve the control performance by using additional parameters to capture the more complicated behavior of complex nonlinear systems. The proposed ET-MFAC methods only rely on the linear data models directly obtained from data without using any other mechanistic model information. The validity of the three ET-MFAC methods is confirmed through both theoretical analysis and simulation studies.

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input-output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC.

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.

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, 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.

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 new data-driven ILC method is proposed for I/O constrained nonlinear systems. An iterative dynamic linearization is introduced for the controlled nonlinear systems. All of the constraints on the system inputs and outputs are reformulated with a linear matrix inequality. The learning control law is then developed by minimizing a predesigned cost function subjected to the linear matrix inequality constraint. Simulation results illustrate the effectiveness of the proposed approach.

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.

Using a technique of sampled-data transformation for differentiation and integration, a sampled-data adaptive iterative learning control is presented for a class of nonlinear systems. The main control structure is designed by a fuzzy system used as a function approximator to compensate for an unknown certainty equivalent controller. The robustness problem due to function approximation error and input disturbance is solved by a technique of time-varying boundary layer which is utilized to construct an auxiliary error function for adaptive law design. Stability and convergence of the learning system is proved via a Lyapunov-like analysis if the adaptation gains satisfy a convergence condition. Since the convergence condition depends on the upper bound of system unknown input/output coupling function, an identifier based on fuzzy system design is further proposed to estimate the unknown bound. The adaptive laws for the fuzzy parameters are investigated to guarantee that identification error will asymptotically converge to zero. Finally, a numerical example is given to demonstrate the effectiveness of the iterative learning control system.

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.

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.

In this paper, an iterative learning control approach is developed for a class of uncertainty nonlinear discrete-time systems based on the identification of the controlled system. At first, the linearized model of the nonlinear system is proposed. And then using the identification method, we present an indirect iterative learning control scheme for the controlled system. Analysis shows that the scheme can guarantee the system convergence under some conditions.