In this paper, we study the data-drivenH∞ optimal control problem for output synchronization of heterogeneous multi-agent systems via a computationally efficient reinforcement learning (RL) method. Unlike the existing RL control results which solve for the optimal controller through the vectorization and Kronecker product (VKP) operations where the large size of the Kronecker product increases computational complexity, a computationally efficient data-driven RL control method is studied in this paper. First, the optimal output synchronization problem is transformed into anH∞ optimal control problem by constructing an internal model-based distributed control protocol. Then, the corresponding algebraic Riccati equation for theH∞ optimal control is reformulated as a generalized Sylvester-transpose matrix equation (GSTME) at each iteration. To solve the GSTME, thematrixform of the conjugate gradient least squares algorithms that do not require the VKP operations is proposed based on the system dynamics and measurement data of multi-agent systems, respectively. Furthermore, the initial stabilizing gain required for policy iteration learning is proposed based on a data-based solution method. Finally, the feasibility of the designed algorithms is demonstrated through a numerical simulation, and its better computational efficiency compared to existing methods is shown.

This article investigates the model predictive tracking control problem for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. First, in order to alleviate the online computational burden of the MPC algorithm, a simplified model-based predictive strategy is developed, where the nominal system is approximated by a known linear time-varying (LTV) model, enabling the online optimization to be formulated as a quadratic programming (QP) problem. Thereafter, to ensure recursive feasibility and bounded tracking errors under fuzzy approximation errors and bounded disturbances, a Lyapunov-based dynamically updated tracking error constraint is introduced. Furthermore, by converting the original ellipsoidal constraints into relaxed box constraints, computational complexity is further reduced without violating the Lyapunov-based guarantees, which is ensured by an auxiliary one-step optimizer incorporated in the online part of the proposed framework. Compared with existing results, the proposed approach maintains bounded tracking errors with relatively high computational efficiency. The effectiveness of the proposed MPC framework is then demonstrated through simulation results.

This work presents a novel adaptive sampled-data backstepping control method for the fractional-order air handling units (AHUs) in the building heating, ventilating, and air conditioning (HVAC) systems to achieve indoor temperature regulation. The control for fractional incommensurate AHUs, which relieve computational costs for implementing control and thus enhance building energy efficiency due to the concise and precise form of the system model in comparison to the integer-order case, are studied for the first time. By strictly considering the infinite-memory and hereditary characteristics of fractional-order systems, the temperature control scheme, which novelly combines the sampled-data scheme with the backstepping technique for reducing control and transmission resources, is proposed. It is proven on the basis of Lyapunov stability analysis to be effective with the indoor temperature being able to track the target temperature accurately while all the closed-loop signals remain globally bounded even with practically time-varying AHUs system uncertainties and external disturbances. Simulation studies verify the efficacy of the proposed strategy and validate the established results.

Vehicle platoon control is one of the promising technologies to improve the performance of transportation systems. However, communication connections among vehicles in cyber physical vehicle systems (CPVS) are often intermittent due to environmental factors and limitations of physical equipment. Moreover, the system models of the vehicles are generally unknown in practice, making it challenging to implement platoon control for CPVS. To address these challenges, we investigate the challenge platoon control problem for CPVS with intermittent communication, where the system models of both the leader vehicle and the follower vehicles are unknown. A data-driven-based learning algorithm is first designed to obtain the unknown leader model. Then, based on the learned leader model, a finite-time distributed observer is proposed to estimate the leader vehicle state in finite time under intermittent communication. Furthermore, with the unknown system models, a data-driven-based controller gain learning algorithm is proposed to learn the controller gain. Based on the learned controller gain, adaptive decentralized tracking controllers are designed to perform platoon control for CPVS. Finally, the effectiveness of our result is examined by a simulation example.

In this paper, a distributed nonconvex cooperative optimization problem is considered for mobile robot systems (MRSs) under denial-of-service (DoS) attacks. Compared with the existing distributed optimization algorithms, a novel hierarchical design method is adopted, which can be divided into three parts, i.e., resilient distributed nonconvex optimization algorithm design, low-pass filters design, and backstepping-based controller design. Specifically, a resilient distributed nonconvex optimization algorithm is proposed, which ensures convergence to the optimal value under the assumption that the global cost function satisfies the Polyak-Łojasiewicz (P-Ł) condition. This condition imposes more relaxed requirements than the strong convexity assumption. Then, low-pass filters are designed to generate a new state variable with well-defined second-order time derivatives. Additionally, a backstepping-based controller is designed for MRSs with external disturbances, which ensures that MRSs can track the optimal value. Finally, a simulation example is presented to verify the effectiveness of the proposed methods.

In this paper, a data-based containment control method is proposed for multi-agent systems where the system parameters of both leaders and followers areheterogeneousandunknown. Based on the collected data from the leader systems, the least square method is first utilized to identify the parameters of the leaders. Then, the data-based adaptive distributed compensator is designed for each follower to estimate the system parameters and the states of theheterogeneousleaders. Meanwhile, the collected data from follower systems is used to construct the local observer and establish the data-based linear matrix inequalities to determine the observer gains and feedback gains. On the basis of the collected data from leader and follower systems, the data-based adaptive solutions to the output regulation equations are provided. Furthermore, the data-based containment control protocols are designed to realize that the outputs of the followers converge to the convex hull formed by the unknown heterogeneous leaders. Finally, the effectiveness of the proposed data-based control scheme is illustrated by the simulation of the numerical example and the interconnecting RLC circuits.

This article investigates resilient source seeking problem of second-order multirobot systems (MRSs) under mixed cyberattacks, which consist of misbehaving and Denial-of-Service (DoS) attacks. The misbehaving attacks can cover several types of malicious attacks, such as false data injection, stubborn, and Byzantine, while the network connectivity may be compromised by DoS attacks, potentially resulting in a time-varying and disconnected digraph. To this end, a resilient source seeking algorithm is proposed by designing an auxiliary point for each agent such that the coordination problem is transformed into a point tracking one. A reference velocity is calculated to guide benign robots toward the source, leveraging their historically optimal positions with the highest signal strength. This ensures the auxiliary points converge to the source, clustering benign robots nearby. When DoS attacks occur on some edges, the latest sampling data acquired before the attacks is used to hold the control signals for the robots. Then, sufficient conditions are established through rigorous stability analysis. In comparison to existing methods, the proposed approach extends the safe-kernel-based resilient consensus algorithms to a resilient source seeking algorithm for a general discrete-time second-order dynamics, while also can withstand a mixed cyberattack comprising both misbehaving and DoS attacks. Finally, simulation and experimental results are presented to validate the efficacy of the proposed algorithm.

In this article, the fixed-time resilient distributed Nash equilibrium (NE) control problem is addressed for nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks. Unlike existing results on NE seeking in noncooperative games, this article first investigates the layered fixed-time resilient distributed NE control problem for nonlinear MASs against DoS attacks, independent of initial conditions. To address these challenges, the novel layered NE control strategy is proposed, comprising a resilient fixed-time distributed NE seeking algorithm layer, an improved fixed-time performance enhancement layer, and an adaptive controller design layer. Specifically, a fixed-time resilient distributed NE seeking algorithm is first designed to guarantee players actions to converge toward the NE against DoS attacks. Then, novel high-order fixed-time filters are proposed to generate improved actions with smooth characteristics and converge to the actions in the aforementioned fixed-time algorithm. Based on the developed filters, a decentralized fuzzy adaptive controller is developed to achieve bounded tracking within the fixed time using the backstepping technique. Finally, a numerical simulation is conducted to validate the efficacy of the developed method.

This article investigates the resilient distributed Nash equilibrium (NE) control problem for nonlinear multiagent systems (MASs) that suffers from denial-of-service (DoS) attacks in the communication network. Different from the existing works on NE seeking in noncooperative games, it is the first trial to consider the resilient distributed NE control problem for nonlinear MASs under DoS attacks. To overcome the challenges caused by the considered problem, a new layered NE control method is developed, which consists of a resilient distributed NE seeking algorithm, two-stage cascade filters, and a resilient adaptive controller. Specifically, the resilient distributed NE seeking algorithm is proposed to ensure that the actions in this algorithm converge to the NE even under DoS attacks. Then, the improved actions with smooth characteristics are designed by introducing novel two-stage cascade filters. By using newly designed actions and their derivatives, a resilient adaptive controller is proposed to ensure that the output of MASs converges to the NE. Finally, simulation results are provided to verify the effectiveness of the proposed strategy.

In this article, the cooperative fuzzy tracking control problem for a type of high-order nonlinear MASs under the Round-Robin (RR) communication protocol is solved. To effectively reduce the communication among agents, an RR communication protocol is first proposed, where each agent can communicate with only one neighbor at any given time. Based on the developed communication protocol, a hierarchical control approach is introduced, consisting of a distributed observer layer that utilizes information from both local and neighboring agents, and a decentralized control layer that operates solely based on local agent information. Specifically, a distributed observer is designed in the distributed observer layer to achieve the distributed observation objective by introducing a time-varying gain in the observer input. Furthermore, an improved distributed observer with the upper triangular form is constructed to produce a signal with high-order derivatives. In the decentralized control layer, fuzzy adaptive controllers are designed for all agents by using the backstepping technique. By using the Lyapunov stability theory, rigorous stability analysis shows that the cooperative fuzzy tracking control problem is solved under the developed hierarchical control approach. In the end, a simulation example is presented to demonstrate the validity of our proposed method.

In this article, a distributed secure state estimation methodology is presented for Lipschitz nonlinear cyber-physical systems under deception attacks. By using the locally observable decomposition and the estimate communication with neighbors, secure sate estimation can be achieved under joint observability. Different from the existing results, an adaptive mechanism is developed so that the deception attacks can be compensated on the observer estimation performance. Moreover, the adaptive mechanism is designed in an independent structure to the main state observer which offers more freedom for both attack-free and attacked situations. Finally, simulation results are provided to verify the effectiveness of the proposed method.

This paper addresses the problem of vehicle platoon control for third-order nonlinear cyber physical vehicle systems (CPVSs) within finite-time under denial-of-service (DoS) attacks. Unlike existing approaches that assume known systematic matrix of the leader vehicle, this study proposes a data-driven learning algorithm to learn unknown systematic matrix of the leader vehicle. Additionally, a finite-time distributed observer is introduced, thereby enabling follower vehicles to achieve finite-time state observation of the leader vehicle under DoS attacks. Moreover, a novel low-pass filter chain is designed to construct a new variable with high-order derivatives. Utilizing the new variable, a finite-time resilient decentralized controller is formulated, incorporating fuzzy adaptive methods and backstepping techniques to achieve finite-time vehicle platoon control under DoS attacks. Finally, simulation experiments validate the effectiveness of the proposed method.

In complex traffic environments, the driving performance of the leader vehicle in a platoon can be greatly impacted by sudden and unexpected changes in vehicle acceleration rates. This phenomenon is known as unknown jerk dynamics (JDs), and it can lead to more extreme car-following behaviors (CFBs) in platoon tracking control, which may raise safety and traffic capacity issues. To tackle these concerns, this work studies cooperative platoon tracking control and intermittent optimization problems for connected autonomous vehicles (CAVs) with unknown reaction time delays (RTDs) using a nonlinear car following model (NCFM). In a free-design but directed communication network, we assume that the leader CAV’s external inputs have unknown but bounded parameters both for the JDs and RTDs, while only a small number of nearby follower CAVs are aware of the leader CAV’s acceleration signals. To solve these issues, we consider that each follower CAV implements a distributed observer law, which provides a reference signal stated as an estimated JD of the leader CAV. Then, a distributed platoon tracking control protocol is proposed to construct cooperative tracking controllers with identical inter-vehicle constraints (ICs). This maintains the desired safety distance between the CAVs and allows each follower CAV to track its leader CAV only through local information exchange. In addition, we present a robust intermittent optimization design and a novel intermittent sampling condition that can guarantee optimally scheduled feedback gains for the cooperative platoon tracking controllers to minimize the control cost in the presence of unknown JDs and RTDs under non-identical ICs. Simulation case studies are conducted to demonstrate the effectiveness of the proposed approaches. We also demonstrate the efficient development of such a distributed cooperative car-following model for the platoon’s motion (or as an intelligent speed advising system for automated or human-driven vehicles), resulting in a trip that is safe, comfortable, and energy efficient.

This paper addresses the data-driven safe prescribed performance lane-changing control problem of vehicle platoons with unknown dynamic models. As the safe guarantee for the lane changing, the collision avoidance condition is built among the vehicle platoon and surrounding vehicles firstly. Then, a desired collision-free driving trajectory is designed for the leader vehicle, which guides the vehicle platoon to complete the lane changing under the time-varying output constraint. To remove the dependence on the system output at the next time in the controller design of the existing work, a novel dynamic linearization data model is developed to relate the unconstrained prescribed performance tracking error to the system input. Based on these developments, a creative data-driven prescribed performance lane-changing control scheme is proposed only using the input-output data for the first time. Through the rigorous proof, the controlled vehicle platoon can safely complete the lane-changing maneuver with the pre-given accuracy within predefined finite time step. Finally, a vehicle platoon example with the comparative analysis is provided to validate the effectiveness of the proposed lane-changing control algorithm.

This article investigates the distributed control problem for nonlinear multiagent systems (MASs) with unknown system models. A novel distributed model-free adaptive learning algorithm is developed to learn a controller from the online system data. Notably, a significant advancement over conventional methods is that the proposed algorithm requires only local interaction data from neighboring agents, eliminating dependencies on both a priori system structural knowledge and global topology information. Comprehensive simulations validate the theoretical results and demonstrate the superior efficacy of the devised algorithm.

This article investigates the robust data-driven containment control problem for heterogeneous multiagent systems where the system dynamics of both the leaders and the followers are unknown. During the data collection phase, the follower systems are disturbed by unmeasurable but bounded noises. A data-based linear matrix inequality condition is first constructed from the noisy data to determinate the feasible feedback gain for each follower. Then, the distributed observer which is independent of the system matrix of the leaders is designed to estimate the convex hull of the leaders. Moreover, the approximate solution to the linear matrix equation for heterogeneous system is solved with bounded approximate error where the noisy data of each follower and the normal data of arbitrary leader is utilized. Based on the proposed feedback gain and observer as well as approximate solution, the robust data-driven control protocol is provided to guarantee the uniform boundedness of containment error. Finally, a numerical example and a multivehicle model are given to verify the effectiveness of the designed containment control protocol.

In this article, the problem of piecewise fault detection (FD) for continuous-time piecewise linear (PWL) system with measurement outliers via new event-triggered (ET) mechanisms is investigated. First, piecewise FD observer with adaptive saturation of output errors is designed to mitigate the effect of outliers on the residual signals, such that false alarms are avoided through the established FD scheme. Then, based on the presented piecewise FD observer, a new ET design scheme that depends on the different regions where the states of the PWL system and piecewise FD observer are located is proposed, and an ET FD method is studied through the ET mechanisms. Unlike the existing results, the established FD scheme can effectively avoid false alarm caused by outliers, and the piecewise FD observer is designed separately from the new ET mechanisms, while co-design is necessary in the existing results. Finally, the effectiveness of the presented scheme is demonstrated by simulation examples.

In this paper, we investigate the distributed resilient control problem of voltage and frequency restoration in AC microgrids (MGs) subject to false data injection (FDI) attacks under event-triggered communication. To solve the problem, new distributed dynamic event-triggered$k$-step attack observers are primarily designed for the accurate estimation of attacks while avoiding continuous communication. Based on the observer state, cooperative resilient controllers for voltage and frequency restoration are proposed, and the convergence of the voltage and frequency of the AC MGs as well as the exclusion of Zeno behavior are proved theoretically. Different from the existing event-triggered resilient control methods in AC MGs subject to unknown bounded FDI attacks, the developed distributed dynamic event-triggered based$k$-step attack observers and cooperative resilient controllers can guarantee accurate observation and compensation for FDI attacks. Finally, experimental tests are carried out to validate the effectiveness of the proposed control method, which demonstrates great resilience in maintaining stable operations under FDI attacks and represents a dramatic reduction in communication costs.

In this paper, the distributed secondary voltage and frequency restoration problem is addressed in AC microgrid systems subjected to hybrid false data injection (FDI) and denial-of-service (DoS) attacks. Firstly, a new distributed resilient iterative estimator based on the k-step estimation method is proposed that can accurately estimate the FDI attack signals as well as the voltage and frequency of each distributed generation (DG) even under the impact of DoS attacks. Then, based on the mean value of the attack estimation signal, a distributed resilient secondary controller is designed to compensate for the considered hybrid attacks. Compared with existing researches on resilient control of AC microgrids under hybrid attacks, the voltage and frequency regulation errors of the microgrid system converge to zero for the first time. Finally, the precise convergence of voltage and frequency in the AC microgrid system under the proposed method is verified through a real-time controller-hardware-in-the-loop experiment in OPAL-RT.

The neural network-based adaptive backstepping method is an effective tool to solve the cooperative tracking problem for nonlinear multiagent systems (MASs). However, this method cannot be directly extended to the case without continuous communication. It is because the discontinuous communication results in discontinuous signals in this case, the standard backstepping method is inapplicable. To solve this problem, a hierarchical design scheme that involves distributed cooperative estimators and neural network-based decentralized tracking controllers is proposed. By introducing a dynamic event-triggered mechanism, cooperative intermediate parameter estimators are first designed to estimate the unknown parameters of the leader. By using the interpolation polynomial method, these estimators are extended to smooth estimators with high-order derivatives to guarantee that the backstepping method is applicable. Based on the state of the smooth estimators, a backstepping-based decentralized neural network tracking controller is designed. It is shown that the tracking errors are asymptotically convergent and all the signals in the closed-loop systems are bounded. Compared with the existing cooperative tracking results for nonlinear MASs with event-triggered communication, a more general class of MASs is considered in this article and a better performance in terms of asymptotic tracking is achieved. Finally, a simulation example is given to show the effectiveness of our developed method.

This article focuses on distributed nonconvex optimization by exchanging information between agents to minimize the average of local nonconvex cost functions. The communication channel between agents is normally constrained by limited bandwidth, and the gradient information is typically unavailable. To overcome these limitations, we propose a quantized distributed zeroth-order algorithm, which integrates the deterministic gradient estimator, the standard uniform quantizer, and the distributed gradient tracking algorithm. We establish linear convergence to a global optimal point for the proposed algorithm by assuming Polyak-Łojasiewicz condition for the global cost function and smoothness condition for the local cost functions. Moreover, the proposed algorithm maintains linear convergence at low-data rates with a proper selection of algorithm parameters. Numerical simulations validate the theoretical results.

In this paper, the distributed fuzzy tracking control problem is investigated for high-order fuzzy nonlinear multiagent systems (MASs) under denial-of-service attacks. The proposed method is distinct from existing approaches in that it can accommodate scenarios where the model parameters of the reference systems are unknown, and the MAS is high order and nonlinear. Specifically, a data-driven algorithm is first introduced to learn the unknown reference system matrix. Based on the learned matrix, a distributed resilient observer and an improved observer are, respectively, designed to guarantee that both observers can observe the reference system state and that the high-order derivative of the improved observer state exists. By using the improved observer state and its high-order derivatives, a decentralized adaptive fuzzy controller is designed for each agent based on the backstepping technique. It is shown that the distributed resilient tracking can be achieved by the proposed method. Finally, a simulation example is proposed to show the effectiveness of the developed method.

In this paper, we study the cooperative optimization problem (COP) for fuzzy nonlinear multi-agent systems (MASs) subjecting to denial-of-service (DoS) attacks. Unlike the existing cooperative optimization results, both fuzzy nonlinear systems and DoS attacks are considered in this paper. To solve the problem, a hierarchical equivalence mechanism is first introduced to transform the COP into an equivalent one consisting of both a distributed optimization problem (DOP) and a decentralized tracking problem (DTP). By introducing an optimal distributed algorithm, a customized virtual signal is devised to minimize the optimization function and simultaneously mitigate the effects of DoS attacks. To construct a bridge between solving the COP and the DTP, a local reference generator, which includes the characteristics of existing high-order derivatives, is designed utilizing the Hermite interpolation method. Subsequently, the backstepping technique is employed to create a decentralized fuzzy adaptive controller. It is illustrated that the proposed method is capable of achieving the cooperative optimization objective. Finally, the theoretical results are successfully applied to show the efficiency of the proposed method.

In this paper, the prescribed-time cooperative resilient fuzzy tracking control problem is addressed for thirdorder nonlinear cyber-physical vehicle systems (CPVS) under denial-of-service (DoS) attacks. Different from the existing results on cooperative resilient fuzzy tracking control, the developed method can achieve the cooperative resilient fuzzy tracking control objective within the prescribed time. To begin with, a data-driven-based online learning algorithm is introduced for learning the unknown and switching matrix of the reference signal. Based on the learned matrix, novel distributed resilient cooperative observers are designed to achieve prescribed-time observation by introducing an asynchronous observing method. To further improve the smoothness of the observation signal, a new improved smooth second-order prescribed-time observer is designed. Furthermore, leveraging the states of the smooth observer, a fuzzy controller is proposed to achieve precise tracking within the prescribed time, independent of initial conditions using the scaling error method and the backstepping technique. Finally, a simulation example is included to illustrate the effectiveness of the proposed methodology

This article studies the cooperative resilient tracking control problem for nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks and time delays. In comparison to the existing distributed control results based on the output observability condition, a joint output observability condition, which is a more universal one, is considered in this article. Based on this, a novel cooperative resilient observer is designed to estimate the state of the reference system subjected to DoS attacks and time delays in the communication topology. Then, a new observed variable with high-order derivatives is constructed by designing a novel chain of low-pass filters. Furthermore, with the help of the newly constructed variables, a fuzzy controller is proposed by using the adaptive method and backstepping technology to ensure the semiglobally uniformly ultimately boundedness for tracking errors. Finally, a simulation example is included to showcase the effectiveness of the proposed method.

This article studies the distributed quantized tracking control problem with prescribed output performance requirements for uncertain nonlinear integer high-order multiagent systems (MASs) with both Denial-of-Service (DoS) attacks and external unknown disturbances under data-rate-constrained communication networks. A hierarchical control framework including a quantized resilient distributed observer layer and a decentralized quantized adaptive fractional-order controller layer is proposed for solving the considered control problem. Specifically, quantized resilient distributed observers are designed at the observer layer for each agent to guarantee the availability of observing the reference system under the influence of data-rate-constrained communication and DoS attacks. Based on the designed observers, smooth reference trajectories with the existence of high-order derivatives, which ensure the applicability of the backstepping technique, are then constructed at the decentralized controller layer, where a novel adaptive fractional-order prescribed performance-based backstepping quantized control strategy is proposed for high-order integer uncertain systems, resulting in an enhanced control scheme with the integration of fractional calculus. It is theoretically proven that under data-rate constraints and DoS attacks, the output tracking error of each agent in relation to the reference signal will constantly stay strictly within the predefined performance limit under the proposed control scheme, with all closed-loop signals remaining bounded. Simulation studies are provided as evidence to establish the efficacy of the proposed distributed quantized fractional adaptive prescribed performance-based control strategy.

This article studies the data-driven distributed vehicle platoon control problem for heterogeneous nonlinear vehicle systems. The heterogeneous nonlinear vehicle systems are first transformed into the linear data model with the increment form. Then, a novel data-driven distributed cooperative controller is devised to accomplish the vehicle platoon control objective, where the stability analysis problem is converted into the feasibility problem with the help of the linear matrix inequality technique. The main advantage of the devised control algorithm is that it only utilizes the position and speed information of neighboring vehicles and does not require any pre-training process. Finally, simulation is given to demonstrate the devised control algorithm with comparisons.

In this article, we consider the cooperative tracking problem for a class of nonlinear multiagent systems (MASs) with unknown dynamics under denial-of-service (DoS) attacks. To solve such a problem, a hierarchical cooperative resilient learning method, which involves a distributed resilient observer and a decentralized learning controller, is introduced in this article. Due to the existence of communication layers in the hierarchical control architecture, it may lead to communication delays and DoS attacks. Motivated by this consideration, a resilient model-free adaptive control (MFAC) method is developed to withstand the influence of communication delays and DoS attacks. First, a virtual reference signal is designed for each agent to estimate the time-varying reference signal under DoS attacks. To facilitate the tracking of each agent, the virtual reference signal is discretized. Then, a decentralized MFAC algorithm is designed for each agent such that each agent can track the reference signal by only using the obtained local information. Finally, a simulation example is proposed to verify the effectiveness of the developed method.

In this article, a learning-based resilient fault-tolerant control method is proposed for a class of uncertain nonlinear multiagent systems (MASs) to enhance the security and reliability against denial-of-service (DoS) attacks and actuator faults. With the framework of cooperative output regulation, the developed algorithm consists of designing a distributed resilient observer and a decentralized fault-tolerant controller. Specifically, by using the data-driven method, an online resilient learning algorithm is first presented to learn the unknown exosystem matrix in the presence of DoS attacks. Then, a distributed resilient observer is proposed working against DoS attacks. In addition, based on the developed observer, a decentralized adaptive fault-tolerant controller is designed to compensate for actuator faults. Moreover, the convergence of error systems is shown by using the Lyapunov stability theory. The effectiveness of our result is examined by a simulation example.

In this article, an adaptive fractional backstepping controller is designed for integer-order nonlinear uncertain systems of arbitrary order with prescribed performance subject to unknown time-varying disturbances. The integration of fractional adaptive backstepping control procedure and prescribed performance bound technique, which describes the convergence rate and largest overshoot of the output error, into a unitary framework can result in an enhanced control scheme with high precision. Based on Lyapunov analysis, it is theoretically demonstrated that under the proposed control scheme, all the closed-loop signals remain bounded and the output tracking error with respect to the reference signal, which is strictly confined within the specified performance bound for all time, will asymptotically converge to zero. Simulation studies are presented to show the effectiveness of the proposed fractional adaptive prescribed performance-based control strategy.

This work explores the development of backstepping-based adaptive control for a class of nonlinear fractional-order systems that encounter systematic uncertainties, time-varying external disturbances, and quantized control input. A novel analog chain rule computation method is proposed to overcome the difficulty in handling the fractional derivatives of composite functions (i.e., virtual control signals) encountered in intermediate recursive steps of the backstepping procedure. A quantified adaptive controller is strictly crafted to guarantee the stability of the system, with all closed-loop signals staying within bounds and the system output tracking error converging to an adjustable residual set asymptotically, leveraging the direct fractional Lyapunov method and such an approach. The simulated studies confirm the efficacy of the investigated control strategy.

This article addresses the resilient practical cooperative output regulation problem (RPCORP) for multiagent systems subjected to both denial-of-service (DoS) attacks and actuator faults. Fundamentally different from the existing solutions to RPCORPs, the system parameters considered in this article are unknown to each agent, and a novel data-driven control approach is introduced to handle such an issue. The solution starts with developing resilient distributed observers for each follower in the presence of DoS attacks. Then, a resilient communication mechanism and a time-varying sampling period are introduced to, respectively, ensure the neighbor state is available as soon as attacks disappear and to avoid targeted attacks launched by intelligent attackers. Furthermore, a model-based fault-tolerant and resilient controller is designed based on the Lyapunov approach and the output regulation theory. In order to remove the reliance on system parameters, we leverage a new data-driven algorithm to learn controller parameters via the collected data. Rigorous analysis shows that the closed-loop system can resiliently achieve practical cooperative output regulation. Finally, a simulation example is given to illustrate the effectiveness of the achieved results.

This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an$H_{\infty }/H_{\infty }$multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection$H_{\infty }$control problem, necessary and sufficient conditions for designing the$H_{\infty }$suboptimal controller were presented, and the$H_{\infty }$performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

The problem of the model-free adaptive resilient control (MFARC) for nonlinear cyber-physical systems (CPSs) suffered from aperiodic jamming attacks is investigated in this article. First, the MFARC framework subject to aperiodic jamming attacks is established, and an intermediate variable method is introduced to avoid using the unavailable time-varying parameter and further eliminate an extra assumption on the sign limit of it. Then, a MFARC scheme is devised to track the desired output, where the problem of the tracking control can be transformed into solving a feasibility problem, and the controller parameters can be obtained with the aid of the linear matrix inequality technique. What is more, a novel attack compensation mechanism is developed in the MFARC scheme to mitigate the impact of aperiodic jamming attacks. In the last, an example is provided to verify the effectiveness of the devised MFARC scheme.

This article studies the optimized fuzzy prescribed performance control problem for nonlinear nonstrict-feedback systems under denial-of-service (DoS) attacks. A fuzzy estimator is delicately designed to model the immeasurable system states in the presence of DoS attacks. To achieve the preset tracking performance, a simper prescribed performance error transformation is constructed considering the characteristics of DoS attacks, which helps obtain a novel Hamilton-Jacobi-Bellman equation to derive the optimized prescribed performance controller. Furthermore, the fuzzy-logic system, combined with the reinforcement learning (RL) technique, is employed to approximate the unknown nonlinearity existing in the prescribed performance controller design process. An optimized adaptive fuzzy security control law is then proposed for the considered nonlinear nonstrict-feedback systems subject to DoS attacks. Through the Lyapunov stability analysis, the tracking error is proved to approach the predefined region by the preset finite time, even in the presence of DoS attacks. Meanwhile, the consumed control resources are minimized due to the RL-based optimized algorithm. Finally, an actual example with comparisons verifies the effectiveness of the proposed control algorithm.

This article studies the distributed fault-tolerant bipartite output synchronization problem of discrete-time linear multiagent systems (MASs) with process faults under a general directed signed graph. The reference signal is generated by an autonomous exosystem, which can also be seen as a leader. All followers are divided into two subgroups with antagonistic interactions, and the followers in each subgroup are cooperative. We aim to solve the bipartite fault-tolerant control (FTC) problem via the output regulation theory such that bipartite output synchronization can be achieved in the presence of process faults, that is, the outputs of followers with different subgroups can approach the output of exosystem with the same magnitude and the opposite sign regardless of process faults. To estimate the states and the faults of each follower, a simultaneous state and fault estimator based on the neighboring signed output estimation error and the standard discrete-time algebraic Riccati equation (ARE) is designed. Besides, a new exosystem observer with two classes of convergence conditions relying on the respective solutions of standard and modified AREs is provided. All eigenvalues of the exosystem matrix can lie completely outside the unit circle. Based on these estimations, we present a distributed fault-tolerant output feedback controller, which can overcome the no-loops constraint. Finally, simulation results are given to demonstrate the analytic results.

The information exchange among distributed energy resources (DERs) in microgrids (MGs) is through sensing and communication systems, which are prone to expose cyber-attack threats. This article investigates the stability issue of MG systems with distributed secondary control under latency attacks and random denial-of-service (DoS) attacks. Considering these two kinds of attack modes, the corresponding attack consequences including network jamming and time-varying latency in the communication network are simultaneously studied. First, a new metric is defined to quantify the DoS attacks by considering different network jamming choices. Then, the time-domain stability study is conducted considering both attack consequences. Next, a cyber-resilient control strategy is proposed with two control modes: 1) An adaptive-gain resilient controller to sustain the fast stabilization of MG systems under nonuniform time-varying latency attacks, which is proved by the stochastic stability analysis using Lyapunov–Krasovskii functional method. 2) An event-trigger topology reconfiguration controller against excessive latency and damaged cyber connectivity caused by DoS attacks. A switching mechanism for coordinating the above control modes is also designed to guarantee the secondary control functions of MG systems. A modified IEEE 13-bus MG system with five DERs is tested and the effectiveness of the proposed controller under different attack scenarios is verified by OPAL-RT real-time tests.

This article addresses the distributed model-free adaptive control (DMFAC) problem for learning nonlinear multiagent systems (MASs) subjected to denial-of-service (DoS) attacks. An improved dynamic linearization method is proposed to obtain an equivalent linear data model for learning systems. To alleviate the influence of DoS attacks, an attack compensation mechanism is developed. Based on the equivalent linear data model and the attack compensation mechanism, a novel learning-based DMFAC algorithm is developed to resist DoS attacks, which provides a unified framework to solve the leaderless consensus control, the leader-following consensus control, and the containment control problems. Finally, simulation examples are shown to illustrate the effectiveness of the developed DMFAC algorithm.

The problem of the observer-based fully distributed containment control for multiagent systems (MASs) subject to denial-of-service (DoS) attacks is investigated in this article. First, a switched fully distributed control framework is established for a class of DoS attacks constrained by the attack duration. Then, a novel attack-resilient control scheme is developed to accomplish the containment control task. The major advantages of the devised control scheme are that any information of the whole network topology structure is not involved and only the information from neighbor agents is used. What is more, a novel observer-based attack compensator is devised to resist DoS attacks. Finally, a practical example of the mobile robot system is presented to testify the validity of the designed control scheme by a comparison.

This article investigates the prescribed performance security control problem for nonlinear systems subject to denial-of-service (DoS) attacks. An attack compensator is adopted to model the unavailable output signal when the attack is active. Based on the designed attack compensator, a fuzzy estimator is developed to approximate the unmeasurable state variables. Further, a security tracking control method is proposed by combining the fuzzy estimator and the novel attack-dependent barrier Lyapunov function. It can steer the tracking errors to the predetermined neighborhood around the origin in the predefined settling time. Meanwhile, all the closed-loop signals are bounded under DoS attacks. Compared with the existing conclusions with DoS attacks, the tracking accuracy and the time of achieving the tracking can be given in advance. Finally, two comparison simulations verify the validity of the designed security controller.

In this article, we study the adaptive fault-tolerant control (FTC) for multiagent systems (MASs) under denial-of-service (DoS) attacks and actuator faults. The mixed connectivity-maintained/broken attack containing both connectivity-maintained and connectivity-broken attacks is considered, which results that the MASs are with switching topologies. Also, characteristics of DoS attacks, such as durations and frequencies of attacks, make it more difficult to design fault-tolerant controllers and analyze the stability for MASs with node faults. A novel FTC strategy is presented to compensate for node faults. Then, by using the Lyapunov stability analysis, an average dwell-time condition is presented for the bounded synchronization of MASs under DoS attacks. An example of nonlinear forced pendulum systems is proposed to verify the proposed approach.

In this paper, we consider the problem of resilient economic dispatch for power grid under denial-of-service (DoS) attacks. By introducing a resilient distributed economic dispatch algorithm, the minimum of the generation cost can be found while balancing the supply and demand. The global information is estimated by the resilient consensus protocol in a distributed fashion and the optimal solution of the economic dispatch problem is searched by the saddle point dynamics. It is shown that the developed resilient algorithm can ensure the exponential convergence of the closed-loop systems by using the Lyapunov stability theory. Finally, an illustrative example based on the IEEE 9-bus attacked by multi-channels DoS is provided to verify the effectiveness of the proposed method.

In this paper, based on sampled-data control method, we address the stabilization problem for a general class of linear continuous-time fractional systems whose solution contains the Mittag-Leffler function that does not obey the basic exponentiation identity. By considering the infinite memory and hereditary characteristics of fractional-order calculus, we propose a sampled-data controller that guarantees the resulting closed-loop system to be asymptotically stable. Simulation examples are presented to demonstrate the effectiveness of the proposed controller and verify the established results.

In this article, we investigate the distributed resilient observers-based decentralized adaptive control problem for cyber-physical systems (CPSs) with time-varying reference trajectory under denial-of-service (DoS) attacks. The considered CPSs are modeled as a class of nonlinear multi-input uncertain multiagent systems, which can be used to model an AC microgrid system consisting of distributed generators. When the communication to a subsystem from one of its neighbors is attacked by a DoS attack, the transmitted information is unavailable and the existing distributed adaptive methods used to estimate the bound of the n th-order derivative of the reference trajectory become nonapplicable. To overcome this difficulty, we first design a new distributed estimator for each subsystem to ensure that the magnitude of the state of the estimator is larger than the bound of the n th-order derivative of the reference trajectory after a finite time. By employing the estimator state, a distributed observer with a switching mechanism is proposed. Then, a new block backstepping-based decentralized adaptive controller is developed. Based on the DoS communication duration property, convex design conditions of observer parameters are derived with the Lebesgue integral theory and the average dwell time method. It is proved that the output tracking errors will approach a compact set with the developed method. Finally, the design method is successfully applied to show the effectiveness of the proposed method to solve the power sharing problem for AC microgrids.

This article studies the observer-based event-triggered containment control problem for linear multiagent systems (MASs) under denial-of-service (DoS) attacks. In order to deal with situations where MASs states are unmeasurable, an improved separation method-based observer design method with less conservativeness is proposed to estimate MASs states. To save communication resources and achieve the containment control objective, a novel observer-based event-triggered containment controller design method based on observer states is proposed for MASs under the influence of DoS attacks, which can make the MASs resilient to DoS attacks. In addition, the Zeno behavior can be eliminated effectively by introducing a positive constant into the designed event-triggered mechanism. Finally, a practical example is presented to illustrate the effectiveness of the designed observer and the event-triggered containment controller.

This article discusses the prescribed performance control problem for multiagent systems involving the state triggering and the controller output triggering simultaneously. To successfully apply the backstepping technique in the event-triggered control design, the virtual control signal is constructed by the original system state. Compared with the existing results on the prescribed performance, a new barrier Lyapunov function is developed with considering the characteristics of multiagent systems, and a fuzzy adaptive event-triggered control protocol is proposed by the backstepping procedure. It guarantees that the consensus tracking error converges to a predefined region of the origin in a preset finite time. At the same time, all other closed-loop signals remain bounded without the Zeno behavior. Finally, a simulation example confirms the availability of the developed control scheme with a comparison.

This article proposes an adaptive, optimal, data-driven control approach based on reinforcement learning and adaptive dynamic programming to the three-phase grid-connected inverter employed in virtual synchronous generators (VSGs). This article takes into account unknown system dynamics and different grid conditions, including balanced/unbalanced grids, voltage drop/sag, and weak grids. The proposed method is based on value iteration, which does not rely on an initial admissible control policy for learning. Considering the premise that the VSG control should stabilize the closed-loop dynamics, the VSG outputs are optimally regulated through the adaptive, optimal control strategy proposed in this article. Comparative simulations and experimental results validate the proposed method's effectiveness and reveal its practicality and implementation.

In this article, we consider the distributed fault-tolerant resilient consensus problem for heterogeneous multiagent systems (MASs) under both physical failures and network denial-of-service (DoS) attacks. Different from the existing consensus results, the dynamic model of the leader is unknown for all followers in this article. To learn this unknown dynamic model under the influence of DoS attacks, a distributed resilient learning algorithm is proposed by using the idea of data-driven. Based on the learned dynamic model of the leader, a distributed resilient estimator is designed for each agent to estimate the states of the leader. Then, a new adaptive fault-tolerant resilient controller is designed to resist the effect of physical failures and network DoS attacks. Moreover, it is shown that the consensus can be achieved with the proposed learning-based fault-tolerant resilient control method. Finally, a simulation example is provided to show the effectiveness of the proposed method.

This article considers the distributed adaptive fault-tolerant control problem for heterogeneous linear multiagent systems with actuator faults and nonuniform time-varying communication delays. First, novel distributed switching observers are proposed to estimate the system matrix and the state of the exosystem. The observers allow each agent to share its information with its underlying neighbors only at sampled instants of time, thus making a distinct difference from the existing results that require the exosystem matrix to be accessible to all agents at every continuous instant of time. Second, a sufficient condition is derived such that the observer error systems are exponentially stable under the influence of communication delays among interacting agents. Third, new distributed adaptive fault-tolerant controllers, which promise fewer adaptive parameters, are presented to compensate for the actuator faults. It is shown that the developed controllers are capable to effectively and efficiently solve the cooperative fault-tolerant output regulation problem with reduced computational complexity. Finally, three illustrative examples, including an inverted pendulum system, an electronic double-integrator circuit system, and an AC microgrid system, are presented to show the validity and efficiency of the developed method.

This article is concerned with the consensus formation control problem of a class of networked quadrotor aircraft partially bounded and state-dependent perturbations. A general distributed consensus error model is first developed to formulate the formation behavior of the networked quadrotor aircraft. Then, by using adaptive techniques, virtual position control strategies are proposed to eliminate the impacts of perturbations, so that the following quadrotor aircraft can boundedly track the desired position trajectory with a satisfying pattern. Furthermore, based on the designed virtual position control strategies, the attitude reference angles are constructed and adaptive attitude control strategies are further designed to guarantee that the attitude angles track the reference angles asymptotically. In terms of the asymptotic tracking results of attitude control systems, the bounded consensus formation results are obtained based on the Lyapunov stability theorem. Numerical simulations are carried out to verify the efficiency of the designed position formation as well as attitude tracking control strategies of the networked quadrotor aircraft.

This article is concerned with the event-triggered output consensus problem for heterogeneous multiagent systems (MASs) with nonuniform communication delays. Unlike the existing event-triggered consensus results, more general heterogeneous linear MASs and nonuniform communication delays are considered. To reduce communication among subsystems, novel dynamic periodic event-triggered mechanisms are proposed. By using the event-triggered signals at the previous sampling instant, new distributed observers are designed to eliminate asynchronous behavior caused by nonuniform communication delays. Based on the developed observers, the observer error system is converted into a time-delay system with interval time-varying delays. Besides, a controller is designed by using the states of observers. It is shown that the consensus problem can be solved by the proposed method. Finally, an illustrative example is provided to verify the effectiveness of the developed method.

In this article, we investigate the distributed resilient control problem for a class of cyber-physical systems with communication delays under denial-of-service (DoS) attacks. In contrast to the previous DoS attacks results based on multiagent systems (MASs), a new distributed resilient control approach is proposed for more general heterogeneous linear MASs with nonuniform communication delays. Two types of sampled-based observers are, respectively, proposed. Namely, adaptive distributed observers are designed by introducing a buffer mechanism to eliminate the heterogeneous behavior caused by communication delays while adaptive distributed resilient observers are designed by introducing resilient mechanisms to resist the DoS attacks. Furthermore, a time-varying sampling period sequence is provided to prevent the attacker from identifying the sampling period of the system. Based on the developed resilient observers, a controller is developed. It is proved that the considered problem can be solved by the developed method. Finally, a numerical example is given to illustrate the effectiveness of the obtained result.

As a cyber-physical system (CPS), the security of microgrids (MGs) is threatened by unknown faults and cyberattacks. Most existing distributed control methods for MGs are proposed based on the assumption that secondary controllers of distributed generation units operate in normal conditions. However, the faults and attacks of the distributed control system could lead to a significant impact and consequently influence the security and stability of MGs. In this article, a distributed resilient control strategy for multiple energy storage systems (ESSs) in islanded MGs is proposed to deal with these hidden but lethal issues. By introducing an adaptive technique, a distributed resilient control method is proposed for frequency/voltage restoration, fair real power sharing, and state-of-charge balancing in MGs with multiple ESSs in abnormal condition. The stability of the proposed method is rigorously proved by Lyapunov methods. The proposed method is validated on test systems developed in OPAL-RT simulator under various cases.

The cooperative fault-tolerant output regulation problem of linear heterogeneous multiagent systems with actuator faults under directed network topology is addressed in this article. By introducing a time-varying gain and by using a modification technique, fully distributed observers without utilizing any global information are designed to estimate the state of the exosystem. Specifically, the time-varying gain is introduced to estimate the global information, and the modification technique is leveraged to avoid the strictly increasing behaviors of the time-varying gains. Besides, a new fault-tolerant controller is developed to compensate for actuator faults under directed network topology. Moreover, it is proven that the developed method is effective to solve the considered problem by the Lyapunov stability theory. Compared with the existing cooperative fault-tolerant output regulation results, the more general directed network topology is considered in this article. Finally, an illustrative example is used to demonstrate the effectiveness and efficiency of the developed method.

The fault-tolerant formation control problem of a class of nonlinear multiagent systems with actuator/sensor faults under directed and switching network topology is addressed in this article. The main contributions are as follows: 1) the developed controller is effective to compensate for actuator/sensor faults and unknown nonlinearity simultaneously and 2) in contrast to the existing fault-tolerant formation control results, the more general directed and switching network topology is considered. In particular, by using a fuzzy logic system to approximate unknown nonlinearity and by introducing fault estimators to estimate actuator/sensor faults, a novel distributed fuzzy formation controller is developed. By virtue of introducing a modification technique in adaptive law, the phenomenon of strictly increase in adaptive law caused by actuator/sensor faults and unknown nonlinearity can be avoided. In addition, the uniformly ultimately bounded of the formation errors can be shown by introducing a novel Lyapunov function and a new analysis method. The efficiency of the developed method can be shown by an illustrative example demonstrates.

In this paper, the cooperative formation control problem is investigated for multiple two-wheeled mobile robots with unknown parameters. By combining the hierarchical decomposition and prescribed performance bound (PPB) technique, distributed adaptive formation controllers are designed based on dynamic surface control. It is proved in the Lyapunov sense that all the closed-loop signals are semi-globally bounded and the tracking error converges to a compact set, which can be made arbitrarily small by adjusting the design parameters appropriately. Furthermore, formation maintenance, connectivity preservation and collision avoidance can be achieved with the proposed control scheme. Simulations are also given to verify the effectiveness of the theoretical results.

In this paper, the event-triggered consensus problem of linear multiagent systems with time-varying communication delays is addressed. Different from the existing event-triggered consensus results with communication delays, more general nonuniform time-varying communication delays are considered. To avoid the asynchronous phenomenon caused by nonuniform delays, a novel periodic switching controller is developed. Based on this controller, the resulting consensus error system can be modeled as a periodic switching system. Furthermore, the exponential stability of the consensus error system is derived by utilizing the Lyapunov approach and the dwell-time analysis method. Finally, an illustrative example is presented to demonstrate the effectiveness of the developed method.

In this article, a new distributed learning control approach is proposed to address the cooperative fault-tolerant output regulation problem for linear multiagent systems with actuator faults. First, a distributed estimation algorithm with an online learning mechanism is presented to identify the system matrix of the exosystem and to estimate the state of the exosystem. In particular, an auxiliary variable is introduced in the distributed estimation algorithm to construct a data matrix, which is used to learn the system matrix of the exosystem for each subsystem. In addition, by resetting the state of the estimator and by using the identified matrix to update the estimator, all subsystems can reconstruct the state of the exosystem at an initial period of time, which is used for the neighbor subsystem to learn the system matrix of the exosystem. Based on the designed estimator, a novel distributed fault-tolerant controller is developed. Compared with the existing cooperative output regulation results, the system matrix of the exosystem considered in this article is unknown for all subsystems. Finally, a simulation example is provided to show the effectiveness of the obtained new design techniques.

The leader-following consensus problem for linear multi-agent systems with matched unknown nonlinear and actuator faults under switching topology is addressed in this paper. The main contributions are as follows: (1) In contrast to the existing results under switching topology, the unknown nonlinear considered in this paper are completely unknown; (2) The developed controller is capable of compensating for the actuator faults and the nonlinear simultaneously. To be more specific, by approximating the nonlinear by a fuzzy logical system (FLS) and by introducing switching mechanism in the distributed controller and adaptive update laws, a new FLS-based distributed adaptive controller is developed. By virtue of estimating the norm of weight vector in the FLS, the developed controller can compensate for unknown nonlinear under the actuator faults. In addition, it is proven that the developed controller can guarantee that the consensus errors are uniformly ultimately bounded. An illustrative example demonstrates the effectiveness and efficiency of the proposed method.

This paper considers the distributed adaptive output feedback consensus problem for linear multiagent systems with matched nonlinear functions and actuator bias faults under directed communication topology. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Unlike the existing results, the dimensions of output and input vectors considered in this paper may be different by exchanging the order of fuzzy basis functions and weight vectors in fuzzy logic systems. By introducing adaptive mechanisms, a distributed adaptive fuzzy output feedback controller is designed, which only depends on the information from neighbors. In addition, it is shown that all signals in the resulting closed-loop system are uniformly ultimately bounded. Finally, a simulation example is presented to illustrate the effectiveness of the developed method.