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 article devotes to investigate the fuzzy optimal consensus problem for multiagent systems (MASs) subject to denial-of-service (DoS) attacks by using the dynamic event-triggered (DET) strategy. The interval type-2 (IT2) fuzzy systems are employed to model the MASs, which combines with the DET fuzzy controller to establish a closed-loop system. Moreover, two piecewise functions are designed, and the triggered interval in a DoS period is decomposed into some subsets with a sampling interval. Therefore, the closed-loop system is reconstructed to facilitate stability analysis. The piecewise Lyapunov-Krasovskii functional is designed, and the system stability is deduced with and without DoS attacks, respectively. By considering the relationship of the piecewise Lyapunov functional, all agents are ensured to be exponentially stable, and the closed-loop system satisfies an optimal control performance. Two examples show the feasibility of the proposed theory finding. Note to Practitioners—Cyberattacks lead to control failure or data breach of MASs due to data tampering and communication interruption. Besides, the controller based on DET mechanism can save limited network resources. Hence, this research focuses on MASs with parameter uncertainties under DoS attacks in interval type-2 fuzzy form, and a DET fuzzy control scheme is proposed to guarantee system security. The Lyapunov-Krasovskii functional with sampling information is constructed to promote stability verification, and slack matrices are also introduced. This study aims to reveal the design principles of DET fuzzy secure control scheme for MASs under DoS attacks. The conducted stability analysis and DET strategy adapt to the background of engineering application.

This paper proposes an adaptive iterative learning control (AILC) scheme for multiagent systems (MASs) to improve the containment control performance. To deal with the uncertain nonlinearity, a neural network (NN)-based iterative predictor with the same structure of MASs is constructed, where an auxiliary approximation term is further incorporated to handle the NN reconstruction error. By utilizing the output of iterative predictor, an AILC-based containment control scheme is designed under the backstepping framework. To overcome the initial error problem, distributed compensation signals are developed to compensate for containment errors and dynamic surface errors. Instead of using dynamic information of neighbors, only the output of neighbors is used in each follower such that the communication load is reduced. It is established that as iteration index approaches infinity, the iteratively convergence of containment errors is achieved, and the stability of MASs is ensured. Simulation results on manipulators verify the effectiveness of both the iterative predictor and the adaptive iterative learning containment controller.

Tower cranes play an important role in construction, whose performance can determine the efficiency and safety of building construction. Payloads (end-effectors) must be transported along desired paths to ensure work efficiency and obstacle avoidance, rather than point to point. In this paper, an end-effector tracking controller is designed for 5-DOF underactuated tower cranes. Based on the proposed system transformation, tower cranes can be described as cascade systems including actuated and unactuated subsystems. A novel nonlinear coupling variable is defined between actuated (positions and speeds of jibs, trolleys and rope lengths) and unactuated (positions and speeds of payload swing angles) states according to position of end-effectors. The developed control strategy is constructed by block backstepping and the stability analysis is given based on approximate linearization to ensure its mathematical rigor. Finally, the developed end-effector tracking controller is applied to an actual laboratorial tower crane to demonstrate its superiority by comparing to the existing control strategies. The experimental results show that the tracking accuracy of payloads is 35.3% and the maximum swing angle of payloads is 62.65% of the existing controllers.

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 article addresses the adaptive iterative learning formation control (AILFC) problem of multiagent systems (MASs) with unmeasurable state subject to Denial-of-Service (DoS) attacks. To alleviate DoS attacks, a neural network (NN)-based compensation mechanism is proposed to learn communication signals, and a learning-based distributed output observer is designed to estimate the leader output. Moreover, an improved extended state observer (ESO) is designed to deal with unmeasurable states and total disturbance. Then, a time-varying boundary layer method with a normalized function is constructed to address the initial error problem. Furthermore, a multiple observer-based AILFC scheme is developed via the backstepping control technique, and the stability analysis of MASs is given by the Lyapunov theory. Finally, a simulation example is shown to illustrate the effectiveness of the developed AILFC algorithm.

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 considers the rapid vibration reduction problem of macro–micro composite positioning stage (MMCPS) using an adaptive neural preassigned-time control strategy. Based on Newton's second law, the MMCPS is modeled as an interconnected system with unknown perturbations, and for the first time, the vibration reduction problem of MMCPS is transformed into a displacement constraint problem. Through adaptive neural network approximation and backstepping control, a preassigned-time controller with a novel performance function-related term is developed, which not only significantly improves the positioning accuracy and reduces the vibration amplitude but also ensures that the displacements of the voice coil motor axis and the stage are constrained to a predefined region in a finite time. Another distinguished feature of the proposed controller lies in the fact that the settling time of the displacement signals can be set as an arbitrary positive value. Moreover, all signals of the closed-loop system are proved to be semiglobally uniformly ultimately bounded. Finally, the feasibility of the designed control strategy is demonstrated via a simulation experiment.

This work focuses on tracking and controlling a distributed platoon consisting of heterogeneous vehicles with an output dead-zone and model uncertainties. The influence of the output dead zone is handled by the Nussbaum function, and the total disturbances of each channel are estimated using extended state observers (ESOs). Moreover, to remove the traditional condition of zero initial spacing errors (ISEs), a modified quadratic spacing policy (MQSP) is established, which can obtain the traffic flow stability (TFS). A distributed platoon control technique is introduced based on MQSP, second-order ESOs, and a backstepping method to achieve internal and string stability. MATLAB simulation results and PRESCAN/SIMULINK co-simulation experiments testify to the effectiveness of the proposed control strategy.

This article focuses on the fixed-time formation control problem for nonlinear multiagent systems (MASs) with dynamic uncertainties and limited communication resources. Under the framework of the backstepping method, a time-varying formation function is introduced in the controller design. To attain the prescribed transient and steady-state performance of MASs, a fixed-time prescribed performance function (FTPPF) is designed and the further coordinate transformation addressing the zero equilibrium point problem is removed. To achieve better approximating performance, a neural network (NN)-based composite dynamic surface control (CDSC) strategy is proposed, where the CDSC scheme is consisted of prediction errors and serial-parallel estimation models. According to the signals generated by the estimation models, disturbance observers are established to overcome the difficulty from approximating errors and mismatched disturbances. Moreover, an improved dynamic event-triggered mechanism and varying threshold parameters are constructed to reduce the signal transmission frequency. Via the Lyapunov stability theory, all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, the simulation results verify the effectiveness of the developed CDSC strategy.

This article investigates the event-driven finite-horizon optimal consensus control problem for multiagent systems with symmetric or asymmetric input constraints. Initially, in order to overcome the difficulty that the Hamilton-Jacobi-Bellman equation is time-varying in finite-horizon optimal control, a single critic neural network (NN) with time-varying activation function is applied to obtain the approximate optimal control. Meanwhile, for minimizing the terminal error to satisfy the terminal constraint of the value function, an augmented error vector containing the Bellman residual and the terminal error is constructed to update the weight of the NN. Furthermore, an improved learning law is proposed, which relaxes the tricky persistence excitation condition and eliminates the requirement of initial stability control. Moreover, a specific algorithm is designed to update the historical dataset, which can effectively accelerate the convergence rate of network weight. In addition, to improve the utilization rate of the communication resource, an effective dynamic event-triggering mechanism (DETM) composed of dynamic threshold parameters (DTPs) and auxiliary dynamic variables (ADVs) is designed, which is more flexible compared with the ADV-based DETM or DTP-based DETM. Finally, to support the effectiveness of the proposed method and the superiority of the designed DETM, a simulation example is provided.

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

In this article, a preassigned finite time control problem of nonlinear systems in strict-feedback form is investigated. From the perspective of arbitrary settling time, an appropriate preassigned finite-time performance function (PFPF) is constructed, and the preassigned finite-time stability (PAFS) is established, where the settling (convergence) time is not only completely unconcerned with initial conditions and design parameters but also more flexible. Furthermore, the backstepping technique and reduced-order observer are used to obtain the preassigned finite-time control scheme. The stability criteria of PAFS are developed to guarantee that the output can quickly converge to an arbitrarily small zone in preassigned time, and all signals of the closed-loop control system are PAFS. In the end, simulation examples verify the effectiveness of the presented method.

This article focuses on the distributed adaptive fixed-time platoon tracking problem for third-order fully heterogeneous nonlinear vehicles. The modified dynamics of each vehicle are constructed, and a practically fixed-time criterion is set up. Moreover, the singularity problem in the fixed-time and finite-time control is addressed well by designing new virtual signals and exploiting the inequality technique and power transformation scheme instead of the approximation method. The distributed nonlinear fixed-time tracking protocol is constructed by virtue of the recursive algorithm, and the design process is simplified by a tracking differentiator. In particular, the upper bound of the settling time has nothing to do with initial conditions. Further, the disturbances are tackled via robust$H_{\infty }$control theory. Finally, simulation tests are contained to illustrate the performance of the proposed protocols.

In this paper, the distributed optimal containment control problem for multiple nonholonomic mobile robots (NHMRs) differential game is studied via reinforcement learning. An approximation-based optimal control strategy is developed to ensure the optimal performance index and avoid the potential collision among agents. Firstly, the collision avoidance problem considered in this paper is addressed by exploiting a consensus-like interconnection on a directed graph and an error transformation function. Then, on the basis of the optimal backstepping technique, a single critic neural network is adopted to obtain the solution of the coupled Hamilton-Jacobi (HJ) equation, in which an improved learning mechanism is constructed to relax the requirement on initial control conditions. In addition, based on the Lyapunov stability theory, it is proved that all signals in the closed-loop optimal control are uniformly ultimately bounded. Finally, the proposed control protocol is applied to NHMRs system, which verifies that the solution of the coupled HJ equation solves the containment problem of differential game.

This article focuses on the distributed cooperative compound tracking issue of the vehicular platoon. First, a definition, called compound tracking control, is proposed, which means that the practical finite-time stability and asymptotical convergence can be simultaneously satisfied. Then, a modified performance function, named finite-time performance function, is designed, which possesses the faster convergence rate compared to the existing ones. Moreover, the adaptive neural network (NN), prescribed performance technique, and backstepping method are utilized to design a distributed cooperative regulation protocol. It is worth noting that the convergence time of the proposed algorithm does not depend on the initial values and design parameters. Finally, simulation experiments are given to further verify the effectiveness of the presented theoretical findings.

In this article, the problem of adaptive tracking control is tackled for a class of high-order nonlinear systems. In contrast to existing results, the considered system contains not only unknown nonlinear functions but also unknown rational powers. By utilizing the fuzzy approximation approach together with the barrier Lyapunov functions (BLFs), we present a new adaptive tracking control strategy. Remarkably, the BLFs are employed to determine a priori the compact set for maintaining the validity of fuzzy approximation. The primary advantage of this article is that the developed controller is independent of the powers and can be capable of ensuring global stability. Finally, two illustrative examples are given to verify the effectiveness of the theoretical findings.

In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated withparticular emphasis on global stability. The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determinea priorithe compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the “explosion of complexity” issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

In this study, a class of finite-time consensus of multiple transmission control protocol/active queue management (TCP/AQM) networks is investigated on the basis of a design idea of multi-agent systems, and for the first time, to our knowledge, a novel congestion control concept with neural networks is proposed. First, the problem statement and design goal of the consensus of multiple TCP/AQM networks is given. Then, a pre-assigned finite-time function is introduced to ensure that the tracking error approaches a pre-defined area within finite time. Furthermore, by combining a barrier Lyapunov function and backstepping technique, a neural network-based distributed adaptive finite-time control protocol for the output consensus of multiple TCP/AQM networks is presented, which can effectively generate the desired controls and ensure that the convergent time of all errors has nothing to do with the initial condition and design parameters. In addition, all signals in the closed-loop system are bounded. Finally, an example is given to further illustrate the effectiveness of the theoretical finding presented.

This article focuses on an annular domain finite-time connectively bounded (ADFTCB) problem for a large-scale system with expanding construction (LSWEC). The LSWEC is built via adding new subsystems into the original system which is operating. Inspired by the notion of finite-time annular domain stability (FTADS), a new concept, ADFTCB, is presented in this article, and it is extended to LSWEC for the first time. First of all, the mathematical models of LSWEC and LSWEC with observer are built, and then the corresponding decentralized state-feedback stabilizers and output-feedback stabilizers with observers are designed with the aid of finite-time Lyapunov theory and linear matrix inequality (LMI) method which can make the closed-loop system ADFTCB. A simulation study is provided to demonstrate the feasibility and effectiveness of the presented strategy.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

This work investigates a finite-time adaptive fuzzy tracking control problem for a class of nonstrict feedback nonlinear systems from a new point of view. A new concept, named finite-time performance function (FTPF), is defined in this paper for the first time. Moreover, a finite-time adaptive state feedback fuzzy tracking controller is derived based on fuzzy approximation, backstepping technique and prescribed performance control (PPC), which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to a prescribed arbitrarily small region within a finite-time interval, and maximum overshoot is not more than a predefined level. In addition, a controller design process is given which is less complex than the existing finite-time control design methods. Three simulation studies are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

A decentralized connective stabilization control problem employing reduced-order observers is solved for complexity large-scale systems with expanding construction. Without changing the original decentralized control laws, a decentralized controller is designed for the resulting expanded system so that the new subsystem added to the original one and the expanding system are robustly connective stable. Furthermore the sufficient condition is derived by using Lyapunov theory and LMI approach. Finally, the proposed method is applied to the AGC design of an expanding power system. The simulation results show both the feasibility and the effectiveness of the proposed decentralized control design.

In this paper, an optimal tracking control approach based on adaptive dynamic programming (ADP) algorithm is proposed to solve the linear quadratic regulation (LQR) problems for unknown discrete-time systems in an online fashion. First, we convert the optimal tracking problem into designing infinite-horizon optimal regulator for the tracking error dynamics based on the system transformation. Then we expand the error state equation by the history data of control and state. The iterative ADP algorithm of policy iteration (PI) and value iteration (VI) are introduced to solve the value function of the controlled system. It is shown that the proposed ADP algorithm solves the LQR without requiring any knowledge of the system dynamics. The simulation results show the convergence and effectiveness of the proposed control scheme.