This paper tackles denial-of-service (DoS) attacks and output constraints in secondary voltage control of islanded microgrids. While existing literature predominantly addresses communication security, it largely overlooks the operational boundaries of power converters. This oversight may result in control saturation, device failure and ultimately, compromised system stability. Furthermore, traditional consensus-based voltage regulation fails to facilitate necessary power interchange among sub-microgrids, limiting its practical applicability. To overcome these limitations, a novel distributed voltage control scheme based on the inclusion principle is proposed. Firstly, a distributed control system model incorporating output constraints is established. The nonlinearities of the system are effectively handled via a barrier Lyapunov function approach, ensuring strict adherence to the output voltage amplitude limits. Secondly, an adaptive state estimator with a switching mechanism is developed to mitigate intermittent communication failures induced by DoS attacks. The controller parameters are then obtained by solving a set of linear matrix inequalities, guaranteeing the semi-global uniform ultimate boundedness (SGUUB) of all closed-loop signals and the ultimate convergence of errors to a neighborhood of the origin. Simulation results verify that the proposed strategy effectively ensures voltage stability while simultaneously satisfying both output constraints and cybersecurity requirements.

To address the issues of insufficient stability, low power allocation accuracy, and resource constraints in dc microgrids, this article proposes a distributed optimal control method based on edge computing. Adaptive dynamic programming method is introduced to address the nonlinear control problem, improving the stability and power allocation accuracy. A three-level cloud-edge-device control framework is constructed to improve system efficiency and flexibility combining distributed control and edge computing. The improved event-triggered control mechanism is designed to reduce unnecessary computation and improve the real-time responsiveness of the system. The practicality of the method is verified using a hardware-in-the-loop simulation platform based on the edge intelligent terminal.

Although rich collection of research results on sensor attack (SA) exist, no attack detection mechanism has ever been designed based on output error information to detect whether an attack has occurred. The primary objective of this article is to build a backstepping adaptive tracking control protocol for heterogeneous nonlinear uncertain multi-agent systems (HNUMASs) with partially SA. A dynamic SA detection mechanism by using output error information of agent only is developed to identify the SA. After locating the attack, to circumvent the effects of unknown time-varying output gain caused by SAs, we introduce the Nussbaum function in backstepping design to compensate the unknown time-varying output gain. The result shows that the developed SA detection mechanism is able to detect the occurrence of attack in a timely manner, while the derived adaptive backstepping tracking controller can effectively handle the adverse effects of SA and ensure that all signals are bounded in the closed-loop system. At last, the effectiveness and benefits of the presented approach are verified by simulation example. Note to Practitioners—This paper aims to achieve the adaptive tracking control for HNUMASs under SA, which can be widely used in practice, such as power systems, vehicular platoon systems, etc. The control protocol consists of a attack detection mechanism and Nussbaum function that compensates for the unfavorable effects caused by SAs. Moreover, the system may also be influenced by uncertainties from its neighboring agents in practical applications. Therefore, an additional estimator is designed in each subsystem to handle the uncertainties involved in its neighbor dynamics. This design avoids the exchange of information related to local neighborhood consensus errors among connected subsystems. A feasible strategy is provided for industrial applications.

The primary objective of this article is to construct a distributed adaptive cooperative fault-tolerant control (FTC) protocol for dynamic output-constrained nonlinear multi-agent systems (MASs) subject to actuator fault and unknown output dead zone (UODZ) in the presence of stochastic false data injection (SFDI) attacks. By establishing a unified universal barrier function (UUBF) upon output, the original constrained system is transformed into a fully equivalent non-constrained system, which not only eliminates the restrictive condition of the constraint boundaries/functions but also solves the output constraints problem without changing the control structure. To circumvent the effects of unknown time-varying output coefficient derived from UODZ, we introduce the Nussbaum function in backstepping design. An adaptive FTC strategy based on the parameter adaptive law compensation approach that does not require the lower and upper bounds of the unknown fault coefficient is developed, and it can tolerate SFDI attacks. The result shows that the derived adaptive backstepping FTC protocol can not only achieve the cooperative control for MASs subject to UODZ under SFDI attacks, but also guarantee that all signals are bounded in the closed-loop system and the output constraints are not violated. Finally, simulation examples validate the validity of the developed schemes.

In this article, a novel online adaptive control scheme is developed for the optimal control issues of integrated electric-gas systems with partially unknown dynamics, by combining the decentralized event-triggered mechanism and adaptive dynamic programming techniques. Initially, the complex electric-gas coupling network is modeled in the state-space form. By virtue of neural networks (NNs), the NN-based identifier and the critic NN are designed to approximate the unknown drift dynamic and the optimal value function in an online fashion, respectively. Subsequently, the decentralized event-triggered control strategies are devised under the identifier-critic framework. Moreover, a novel decentralized event-triggered scheme with the dead-zone operation is proposed, which updates the controller and actuator signals only when the triggering condition is violated. As such, the computation complexity and the waste of communication resources can be significantly reduced. On the foundation of the Lyapunov theory, the uniform ultimate boundedness stability of the closed-loop control system and the exclusion of the Zeno behavior are proven. Finally, the effectiveness of the developed algorithm is verified through two numerical examples.

In this article, a novel adaptive critic learning (ACL) framework is constructed for a class of nonzero-sum (NZS) differential games problem of unknown continuous-time (CT) nonlinear systems with state constraints. First, generalized fuzzy hyperbolic model (GFHM)-based identifiers are established to reconstruct the unknown system dynamics. Then, under the ACL framework, a critic network with secure finite-time experience replay turning law is developed for each player to acquire the Nash equilibrium point solution in finite time while the finite-time stability is guaranteed via Lyapunov analysis. Meanwhile, the persistence of excitation (PE) condition is no longer needed in this work, by introducing an easy-to-check rank condition. Furthermore, by incorporating the immediate cost function associated with each player and the control barrier function (CBF), the algorithm ensures that the system states evolve in a secure environment. Finally, two numerical examples are presented to demonstrate the validity of the developed scheme.

In this article, a novel adaptive dynamic programming algorithm is devised to handle the multiplayer nonzero-sum (NZS) games of completely unknown nonlinear systems, subject to state and input constraints under the dynamic self-triggered mechanism. Initially, in order to eliminate the demand for system dynamics, a generalized fuzzy hyperbolic model based identifier is established, which only relies on input–output data. Then, the equivalent transformation of the reconstructed system is implemented by virtue of barrier functions. With the aid of the nonquadratic utility function, the Hamilton–Jacobi equation of the NZS game is derived. After that, an adaptive critic scheme with experience replay is employed to acquire the Nash equilibrium solution. Furthermore, a novel dynamic self-triggered rule is proposed with the dead-zone operation, which not only significantly reduces source consumption but also overcomes the implementation difficulty of monitoring hardware in the event-triggered mechanism. Moreover, the stability of the system and the uniform ultimate boundedness of the critic weights are guaranteed. Ultimately, two simulation examples are given to validate the feasibility of the developed method.

This article focuses on the bipartite output tracking control for heterogeneous linear multiagent systems under the asynchronous edge-based event-triggered transmission mechanism. First, the distributed bipartite edge-based event-triggered compensator is established to estimate the state of the exosystem. The estimated state of the compensator is the same as the state of the exosystem in modulus and opposite in sign because of the existence of antagonistic communications. To be independent of the topology information, the adaptive compensator with an edge-based event-triggered mechanism is then established. And the observer is proposed to recover the unmeasurable system states. Then, the distributed control scheme based on the compensator and the observer is designed to address the bipartite output tracking problem. Moreover, the results in the signed fixed graph are extended to signed switching graphs. The Zeno behavior of each edge is ruled out. Finally, two numerical examples, one application example and one comparison example, are given to demonstrate the feasibility of the main theoretical findings.

This article presents an improved online adaptive dynamic programming (ADP) algorithm to solve the optimal control problem of continuous-time nonlinear systems with infinite horizon cost. The Hamilton-Jacobi-Bellman (HJB) equation is iteratively approximated by a novel critic-only structure which is constructed using the single echo state network (ESN). Inspired by the dual heuristic programming (DHP) technique, ESN is designed to approximate the costate function, then to derive the optimal controller. As the ESN is characterized by the echo state property (ESP), it is proved that the ESN can successfully approximate the solution to the HJB equation. Besides, to eliminate the requirement for the initial admissible control, a new weight tuning law is designed by adding an alternative condition. The stability of the closed-loop optimal control system and the convergence of the out weights of the ESN are guaranteed by using the Lyapunov theorem in the sense of uniformly ultimately bounded (UUB). Two simulation examples, including linear system and nonlinear system, are given to illustrate the availability and effectiveness of the proposed approach by comparing it with the polynomial neural-network scheme.

This article addresses the decentralized control problem of continuous-time nonlinear large-scale interconnected systems by the means of echo state network (ESN). The interconnected terms between the subsystems are treated as the disturbances added to the system dynamics, then the control problem is solved by the proposed robust controllers. By designing a cost function for the nominal subsystems, the robust controller is obtained by solving optimal controllers. The stability of the interconnected systems is proved by a composite Lyapunov function. The online adaptive dynamic program (ADP) method is employed to solve the transformed optimal problem, where a single ESN is utilized to approximate the critic cost and control policy. The optimal control policies of all the isolated subsystems are obtained simultaneously. The closed-loop stability of the feedback nominal systems is also proved, in a uniformly ultimately boundedness (UUB) manner. In the simulation, a large-scale interconnected system with four subsystems is provided to verify the effectiveness of the proposed decentralized controllers.

This article studies an event-triggered communication and adaptive dynamic programming (ADP) co-design control method for the multiplayer nonzero-sum (NZS) games of a class of nonlinear discrete-time wireless sensor-actuator network (WSAN) systems subject to input constraints. By virtue of the ADP algorithm, the critic and actor networks are established to attain the approximate Nash equilibrium point solution in the context of the constrained control mechanism. Simultaneously, as the sensors and actuators are physically distributed, a decentralized event-triggered communication protocol is presented, accompanied by a dead-zone operation which avoids the unnecessary events. By predefining the triggering thresholds and compensation values, a novel adaptive triggering condition is derived to guarantee the stability of the event-based closed-loop control system. Then resorting to the Lyapunov theory, the system states and the critic/actor network weight estimation errors are proven to be ultimately bounded. Moreover, an explicit analysis on the nontriviality of the interevent times is also provided. Finally, two numerical examples are conducted to validate the effectiveness of the proposed method.

In this article, a novel online decentralized event-triggered control scheme is proposed for a class of nonlinear interconnected large-scale systems subject to unknown internal system dynamics and interconnected terms. First, by designing a neural network-based identifier, the unknown internal dynamics of the interconnected systems is reconstructed. Then, the adaptive critic design method is used to learn the approximate optimal control policies in the context of event-triggered mechanism. Specifically, the event-based control processes of different subsystems are independent, asynchronous, and decentralized. That is, the decentralized event-triggering conditions and the controllers only rely on the local state information of the corresponding subsystems, which avoids the transmissions of the state information between the subsystems over the wireless communication networks. Then, with the help of Lyapunov's theorem, the states of the developed closed-loop control system and the critic weight estimation errors are proved to be uniformly ultimately bounded. Finally, the effectiveness and applicability of the event-based control method are verified by an illustrative numerical example and a practical example.

This article addresses the adaptive bipartite event-triggered output consensus issue for heterogeneous linear multiagent systems. We consider both cooperative interaction and antagonistic interaction between neighbor agents in both fixed and switching topologies. An adaptive bipartite compensator consisting of time-varying coupling weights and dynamic event-triggered mechanism is first proposed to estimate the leader's state in a fully distributed manner. Different from the existing methods, the proposed compensator has three advantages: 1) it does not depend on any global information of the network graph; 2) it avoids the continuous communication between neighbor agents; and 3) it is applicable for the signed communication topology. Assume that the system states are unmeasurable, and we thus design the state observer. Based on the devised compensator and observer, the distributed control law is developed such that the bipartite event-triggered output consensus problem can be achieved. Moreover, we extend the results in fixed topology to switching topology, which is more challenging in that state estimation is updated in two cases: 1) the interaction graph is switched or 2) the event-triggered mechanism is satisfied. It is proven that no agent exhibits Zeno behavior in both fixed and switching interaction topologies. Finally, two examples are provided to illustrate the feasibility of the theoretical results.

In this paper, a novel adaptive dynamic programming (ADP) algorithm is developed for the infinite-horizon (H∞) optimal control problems with unknown continuous-time (CT) nonlinear systems subject to external disturbances. To facilitate the implementation of the algorithm, generalized fuzzy hyperbolic models (GFHMs) are utilized to establish an identifier-critic architecture, where the identifier is designed to reconstruct the unknown system dynamics, and the GFHM-based critic network is employed to approximate the value functions. The CT H∞optimal control issue is converted into a two-player zero-sum game and the corresponding Hamilton-Jacobi-Isaacs equation is derived. The learning procedure of the critic design is adaptively implemented with the help of the reconstructed model, thus the requirement of the complete system dynamics is relaxed. Furthermore, by the means of Lyapunov direct method, the uniform ultimate boundedness stability analysis of the closed-loop control system is explicitly provided. Finally, to compare the control performances and disturbance attenuation properties of the proposed method and the existing ADP algorithms, two numerical examples are given.

This article presents a novel event-driven guaranteed cost control method for nonlinear systems subject to actuator faults. For the purpose of handling the problem of actuator faults and obtaining the event-driven approximate optimal guaranteed cost control approach for general nonlinear dynamics, the reinforcement learning (RL) algorithm is utilized to develop a sliding-mode control (SMC) strategy. To begin with, the unknown faults can be estimated by designing a fault observer. Meanwhile, an SMC technique is presented aiming at countering the effect of abrupt faults. In addition, the optimal performance of the equivalent sliding mode dynamics is considered, then an event-driven guaranteed cost control mechanism is implemented by using RL principle. In the control process, a general cost function, which has a simpler structure, is given to reduce the computation complexity. At the same time, a modified cost function is approximated to obtain optimal guaranteed cost control by using a single critic neural network (NN). In addition, a modified weight update law for critic NN is presented to relax the persistence of excitation (PE) condition. Moreover, a newly triggering condition, which is easy to be implemented, is designed, and the critic NN update law makes sure that the system states are stable. Furthermore, in light of the Lyapunov analysis, it is demonstrated that the developed event-driven control method guarantees the uniformly ultimately bounded (UUB) property of all the signals. Finally, three simulation results are given to validate the designed control method.

In this paper, by incorporating the event-triggered mechanism and the adaptive dynamic programming algorithm, a novel near-optimal control scheme for a class of unknown nonlinear continuous-time non-zero-sum (NZS) differential games is investigated. First, a generalized fuzzy hyperbolic model based identifier is established, using only the input-output data, to relax the requirement for the complete system dynamics. Then, under the event-based framework, the coupled Hamilton-Jacobi equations are derived for the multiplayer NZS games. Then, the adaptive critic design method is employed to approximate the optimal control policies; thus, an identifier-critic architecture is developed to obtain the event-triggered controller. By the virtue of the Lyapunov theory, a state-dependent triggering condition, which is different from the existing works, is developed to achieve the stability of the closed-loop control system both for the continuous and jump dynamics. Finally, two numerical examples are simulated to substantiate the feasibility of the analytical design.