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This paperinvestigates the distributed consensus control for nonlinear multi-agent systems with input quantization in a directed communication topology. A nonsingular adaptive finite-time control (NAFTC) scheme is proposed by combining the filtered backstepping method with neural network control. Both chattering and singularity problems of the control signals are avoided thanks to its C 1 continuity, so that the contradiction between discontinuous- and C 0 continuous finite-time control with input quantization does not exist in our scheme. At the same time, a novel inequality for the input-output relationship of hysteresis quantizer is derived, which can simply handle the input quantization without requiring additional stability analysis. What is more, some common assumptions, such as Lipschitz assumption and Holder-continuity assumption, are not required in our scheme. Finally, stability analysis and numerical simulation are provided. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the distributed leader‐following formation control for nonlinear multi‐agent systems (MASs) subject to compound disturbances. Three aspects of the control objective: formation control, collision avoidance and connectivity preservation are achieved by the designed controller composed of three control laws. The formation control law is developed based on the barrier Lyapunov function and the backstepping method, which can prescribe the performance of the close‐loop system to some extent. Within our scheme, an adaptive finite‐time disturbance observer is used to enhance the robustness of the control system against compound disturbances including parameter perturbations, actuator bias faults and external disturbances. Meanwhile, a nonlinear tracking differentiator is introduced for each follower to cancel complex differential calculations and the requirement for the leader's acceleration information. Furthermore, the auxiliary control laws for collision avoidance and connectivity preservation are designed based on the artificial potential field method, which plays an important role during the formation shaping. Finally, complete stability analysis and vivid numerical simulation are carried out. [ABSTRACT FROM AUTHOR]

The fault-tolerant leader–following consensus problem of multi-agent systems (MASs) with jointly connected topologies is considered in this paper. A control law, which is compensated by adaptive estimation of fault parameters using finite interval projection operator, is designed and enables the MAS with jointly connected topologies to achieve consensus in the presence of actuator faults. Furthermore, compared with the most existing works of fault-tolerant consensus with fixed and switching connected topologies, the results with jointly connected topologies are more general in practical systems. Moreover, the effectiveness of the controller for the considered problem is proved based on the Lyapunov stability theory. At the final part, by a numerical simulation, the validity of the results is verified. [ABSTRACT FROM AUTHOR]

Battery energy storage systems are widely used in energy storage microgrids. As the index of stored energy level of a battery, balancing the State-of-Charge (SoC) can effectively restrain the circulating current between battery cells. Compared with passive balance, active balance, as the most popular SoC balance method, maximizes the capacity of the battery cells and reduces heat generation. However, there is no good solution in the battery management system (BMS) to ensure active balance during distributed charging. In view of this, this paper designs two novel distributed charging strategies based on a kind of smart leader, in which a constant static leader is modified by a dynamic leader. The modified leader is in charge of guiding SoC to converge to the target value and repress SoC imbalance. The maximum and weighed error between the state of the leader and its neighbor cells are used in the two methods, respectively, both in an event triggered manner. When the relevant index exceeds the threshold, the two methods are used to regulate the leader's state. Under this modification, the eigenvalue of the followers' error dynamic system is reduced, and SoCs follow the dynamic leader faster, thus repressing SoC imbalance. Compared with a constant leader, the smart leader pays more attention to improving SoC imbalance. Additionally, to facilitate analysis, a reduced method is applied to transform the system with an unified input time delay into a nondelay system. Several cases are designed to verify the effectiveness of the designed strategies and test it under different parameters and different time delays. [ABSTRACT FROM AUTHOR]

The state of charge (SoC) balance, power sharing, and frequency restoration are common control objectives of battery energy storage systems. However, the SoC balance scheme induced by the power allocation through existing droop controllers can cause the capacity parameters of battery cells to be unequal to the droop coefficient, which is the result of battery capacity degradation. Under this limitation, previous capacity-based droop controllers and the secondary controllers are no longer suitable to address the imprecise power sharing and frequency restoration caused by this problem. Therefore, a power allocation scheme based on the current SoC level ratio is designed to induce a new droop controller and ensure that the SoC simultaneously drops to 0. In order to restore frequency in a distributed manner and obtain the SoC level ratio, a distributed nominal frequency controller, SoC average estimator, and power-sharing controller are designed based on multi-agent systems in both asymptotic and finite-time manners. In the asymptotic scheme, the steady-state performance of the SoC estimator is adjustable, and power sharing and frequency restoration are zero errors. In the finite-time scheme, the influence of parameters on convergence time is well analyzed, and some conservative calculation methods are provided. Several time-domain simulation examples are designed on an improved IEEE-57 bus system to verify the distribution of asymptotic and finite-time schemes. [ABSTRACT FROM AUTHOR]

In this article, the formation control problem is investigated for a class of general first/second‐order discrete‐time heterogeneous multi‐agent systems. Under directed connected topology, a novel formation control protocol is designed by using the relative local information among heterogeneous agents and the formation information in the desired formation. For the discrete‐time heterogeneous multi‐agent systems, some sufficient conditions are derived for reaching the desired formation. If the considered system has the same number of first‐order and second‐order agents, some necessary and sufficient conditions are also obtained by utilizing the bilinear transformation method. Finally, two numerical examples are proposed to demonstrate the feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This article studies the fault-tolerant leader-following consensus problem for multiagent systems with input saturation. The main contribution is to present a modified low-and-high gain feedback approach to deal with multiple actuator faults, including partial loss of effectiveness, outage, and stuck simultaneously. First, without consideration of saturation, a distributed fault-tolerant control scheme is put forward by the adaptive technique, and a practical finite-time stability result is established. Second, by employing the fault-tolerant theory and introducing a novel form of parametric algebraic Riccati equation, a modified low-and-high gain feedback approach is developed for the saturated control strategy. It is proven that the practical finite-time stability can be achieved, and both the steady-state consensus error and the settling time can be well estimated. Finally, numerical simulations are provided to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the leader–follower consensus is investigated for discrete-time second-order multiagent systems with smart leader, where the smart leader can obtain the feedback information from its neighbours. Different from the existing results, an objective function is provided to determine whether the leader utilizes the feedback information from its neighboring agents, with the purpose of making the system have better performance. Under the directed interconnected topology, a novel distributed consensus protocol is designed for second-order discrete-time multiagent systems. Some necessary and sufficient conditions are derived for the leader–follower consensus of discrete-time second-order multiagent systems with smart leader under fixed/switching topology. Finally, two simulation examples are presented to demonstrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the finite‐time consensus tracking problem for second‐order nonlinear multi‐agent systems subject to the actuator bias fault. Based on the sliding mode control and prescribed performance control, two distributed fault‐tolerant consensus protocols are proposed for the sudden bias fault and the slowly varying bias fault of the actuator. The first protocol adopts a passive fault‐tolerant control scheme based on the robustness of the system, which has a simple structure, and is timely and effective against sudden faults. In the second protocol, a novel nonlinear recursive sliding mode surface is designed, and a distributed fault observer is proposed to compensate the influences caused by actuator faults actively. Both of the protocols can prescribe the transient and steady‐state performance of the system. Finally, the performances of the two protocols are verified by two simulation cases for the attitude systems of multiple unmanned underwater vehicles. [ABSTRACT FROM AUTHOR]

In this article, the H∞ consensus tracking problem for multi‐agent systems (MASs) under switching communication topologies is studied. In the objective system, the unknown nonlinear function, exogenous disturbances, and actuator faults are considered. For this problem, a new fully distributed fault‐tolerant control method is developed via utilizing adaptive mechanisms. A sufficient condition is obtained to guarantee the stability of the considered closed‐loop system by topology‐based average dwell time technique combined with Lyapunov stability theory. Unlike the traditional method to estimate the weight matrix, the neural network is used to estimate the norm of weight vectors. Thus, the difficulty that the unknown nonlinear function cannot be compensated when outage or stuck faults occur in some actuators is solved. Compared with the existing controllers for nonlinear MASs, the proposed controller does not require any knowledge about the terms relevant to the global information associated with the network. Furthermore, the proposed controller can compensate for the leader's unknown bounded input and actuator faults. Besides, the closed‐loop system is proven to be stable by the developed controller, and all followers can track the state of the leader. Finally, a numerical simulation is given to validate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

This paper studies the containment control problem for a class of nonlinear multi-agent systems (MASs) with actuator faults (AFs) and external disturbance under switching communication topologies. To address this problem, a new fuzzy fault-tolerant containment control method is developed via utilizing adaptive mechanisms. Furthermore, a sufficient condition is obtained to guarantee the stability of the considered closed-loop system by the dwell time technique combined with Lyapunov stability theory. Unlike the traditional method to estimate the weight matrix, the fuzzy logic system is used to estimate the norm of weight vectors. Thus, the difficulty that the unknown nonlinear function cannot be compensated for when the actuator produces outage or stuck fault is solved. Compared with the existing controllers for nonlinear MASs, the proposed controller is more suitable for the considered problem under the influence of AFs that are detrimental to the operation of each agent system. Besides which, the closed-loop system is proven to be stable by using the developed controller, and all followers converge asymptotically to the convex hull formed by the leaders. Finally, an example based on a reduced-order aircraft model is presented to verify the effectiveness of the designed control scheme. [ABSTRACT FROM AUTHOR]

This article investigates the fault‐tolerant consensus problem for switched multiagent systems with input saturation. Actuator faults including partial loss of effectiveness, outage, bias, and stuck are all considered in switched general linear systems. By utilizing the adaptive projection algorithm, low gain feedback theory, and average dwell time method, novel saturated consensus protocols are designed for both fixed and switching topologies with local information of neighboring agents. It is proven that the fault‐tolerant consensus problem can be solved with the proposed protocols in both leader‐following case and leaderless case. The innovation of this article lies not only in the fact that actuator faults, switched dynamics, and input saturation are simultaneously considered, but also in the fact that a novel modified low‐and‐high gain feedback approach is introduced to deal with various types of actuator faults. Finally, two numerical examples are given to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consensus tracking problem in nonlinear multi-agent systems against external disturbances and multiple actuator faults. The nonlinear dynamics are unknown and the leader's input is unavailable to any follower. By using finite-time Lyapunov stability theory, a distributed discontinuous protocol is developed. On this basis, a fixed-time control protocol is further designed to obtain a settling time regardless of initial conditions. In addition, the practical finite-time consensus and practical fixed-time consensus are investigated by the adaptive technique, under which the bounds of the faults can be estimated online adaptively. The innovation of this work lies in the fact that the finite/fixed-time consensus problem is solved when multiple faults and mismatched nonlinearity are simultaneously considered. The relationship between the settling time and design parameters is well established. Finally, some numerical simulations are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following H ∞ consensus problem for discrete-time nonlinear multi-agent systems with delay and parameter uncertainty is investigated, with the objective of designing an output feedback protocol such that the multi-agent system achieves leader-following consensus and has a prescribed H ∞ performance level. By model transforming, the leader-following consensus control problem is converted into robust H ∞ control problem. Based on the Lyapunov function technology and the linear matrix inequality method, some new sufficient conditions are derived to guarantee the consensus of discrete-time nonlinear multi-agent systems. The feedback gain matrix and the optimal H ∞ performance index are obtained in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics, under the common assumption that each agent can only obtain the relative information of its neighbours intermittently. A kind of distributed protocol based only on the relative local intermittent measurements of neighbouring agents is designed for containment control under fixed directed topology. In the absence of delays, based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee the intermittent containment control of second-order nonlinear multi-agent systems. In the presence of delays, some containment conditions are also obtained for a second-order multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Moreover, the similar results are obtained for second-order nonlinear multi-agent systems under switching directed topology. Finally, simulation examples are given to illustrate the correctness and effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

System modeling is a complex and time-consuming task in engineering, and traditional model-based or observer-based methods are unable to deal situations when the system models are unknown or affected by elements such as temperature. As a result, it is critical to build model-free methods capable of iterative learning and real-time updating. In this paper, a data-driven, model-free TD3-based algorithm is proposed. The neural network is used to address the issue of dimensional explosion in the state and action space. Besides, each agent can set a variable number of neighbors via virtual neighbor technology, giving the connection topology more flexibility. What is more, the proposed controller is only constructed based on the consensus error, which can quickly realize synchronization while consuming the least amount of energy. Finally, proofs and some simulation examples are given to verify the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the containment control problem for second‐order multiagent systems with intermittent communications and time‐varying delays. Under the common assumption that each follower can only communicate with its neighbors over some disconnected time intervals, some distributed controllers are designed such that all the followers can converge to convex hull formed by the leaders. Firstly, a distributed intermittent control protocol without considering time delays is proposed for second‐order containment control with intermittent communications. Then, under delayed and intermittent communication, a kind of distributed containment control algorithm is derived for second‐order multiagent systems with time‐varying delays. Based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee that the second‐order multiagent systems can achieve intermittent containment control under fixed topology. As an extension, similar results are obtained for containment control under switching topology. Finally, numerical simulations are presented to demonstrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In line of the research on leader-following consensus, this paper studies the consensus problem for the first-order multi-agent system with a smart leader. Different from previous works where the leader is independent of all the other agents, a kind of leader, called smart leader, is proposed, which can gain and utilize its neighboring followers' position information. Whether such information will be used in adjusting the control algorithm for the smart leader is decided by an event-trigger function. The theory and simulation results show that the proposed model can gain advantage in robustness and fault-tolerance ability with the traditional one. Moreover, a sufficient condition is provided, which can ensure that the position-tracking error and velocity-tracking error are bounded when some actuator faults occur on some of the followers in the framework of the fixed topology. In addition, similar results are also given under switching topology. Finally, some simulation examples are presented for illustration. [ABSTRACT FROM AUTHOR]

This paper investigates distributed containment control problems for second-order nonlinear multi-agent systems with dynamic leaders. In the presence of bounded unknown nonlinearity, a distributed control algorithm based on High-frequency Feedback Robust Control is proposed. Under this algorithm, a sufficient condition is proposed to ensure that all the followers will converge to the dynamic convex hull formed by dynamic leaders and the containment error can be ultimately bounded for the directed graph where at least one leader has a directed path to each follower and the communication among the followers are undirected. Numerical simulations are also presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The paper deals with the distributed consensus problem of a class of general linear multi-agent systems with time delay. Assuming that the state of the multi-agent system cannot be measured and the output of the multi-agent system is measured discontinuously, a novel impulsive observer is constructed. Based on the impulsive observer, a distributed consensus protocol is proposed for the multi-agent system with a directed communication topology. In view of the hybrid characteristic of the multi-agent system with the impulsive observer, a novel type of piecewise Lyapunov functional which can overcome the jump phenomena at impulsive times is introduced. Based on this, some sufficient conditions in terms of linear matrix inequalities are presented such that the consensus of the multi-agent system can be achieved with an exponential convergence rate. A numerical example under two cases is given to show the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper considers the containment control problem for leader-following multi-agent systems in the presence of dynamically switching topologies with communication delays. Two types of control algorithms are proposed for containment control with first-order dynamics and second-order dynamics. By applying modern control theory and algebraic graph theory, the stabilities of two containment control algorithms are analyzed on Lyapunov–Krasovskii method. Moreover, some sufficient conditions are provided through further researching the connected portion of multi-agent systems, which can ensure that the containment control can be achieved asymptotically when communication topologies are jointly-connected. Finally, some simulation examples are provided to demonstrate the effectiveness of two proposed algorithms. [ABSTRACT FROM AUTHOR]

This article considers a containment control problem for nonlinear multi-agent systems with nonautonomous leaders under directed topology, where each follower may experience various actuator faults and unknown external disturbances. A practical robust fixed-time fault-tolerant controller is proposed that eliminates the adverse effects of disturbances and actuator faults while achieving the containment control objective within a fixed-time. Independent of initial states, a sufficient condition of practical robust fixed-time stabilization is derived, further relaxing the constraint of robust fixed-time stabilization. The combination of sliding-mode control and event-triggered mechanism in this approach provides better control performance. One advantage of this method is that the sliding-mode band size is no longer dependent on the sampling interval but rather on the triggering function. Another advantage is that the resource costs for handling faults are effectively reduced. Additionally, an adaptive boundary layer technique is designed to avoid chattering phenomenon of the discontinuous controller, which utilizes adaptive parameters to autonomously adjust the width of boundary layer. Zeno behavior analysis and a simulated example are also presented. • A sufficient condition for practical robust fixed-time stabilization is derived. • The actuator faults can be efficiently addressed by the containment controller. • The robust fixed-time theory is extended to directed graphs. [ABSTRACT FROM AUTHOR]

• This paper is the first to consider the H ∞ consensus problem for a class of nonlinear MASs with actuator faults in the physical layer and intermittent communications in the cyber layer. To address this difficulty, a distributed robust fault-tolerant control approach by utilizing an adaptive mechanism is revealed. • The designed distributed robust fault-tolerant control can be adjusted online by utilizing an adaptive mechanism with time-varying gains. This illustrates that the new distributed robust fault-tolerant control can be a promising scheme to compensate for both actuator faults and intermittent communications automatically. • A topology-based average dwell time approach is adopted here to deal with the switching jumping issue in the presence of intermittent communications. Besides, the proposed method can handle multiple faults and attenuate the external disturbance for both fixed communication topology and switching communication topology. This paper considers the H ∞ consensus problem for a class of nonlinear multi-agent systems in the presence of multiple faults, including intermittent communications and actuator faults, under the switching communication topologies. Aiming at this problem, a new distributed robust fault-tolerant controller is designed by utilizing an adaptive mechanism to remove the interference of nonlinear functions and multiple faults. Furthermore, the closed-loop system is proven to be stable by applying the topology-based average dwell time technique and the Lyapunov stability theory. Compared with existing controllers for nonlinear multi-agent systems, the developed scheme is efficient for solving the fault-tolerant H ∞ consensus problem of nonlinear multi-agent systems even under the influence of intermittent communications, actuator faults, and switching communication topologies. Finally, an example based on the B747-100/200 aircraft model is given to validate the proposed control scheme's effectiveness. [ABSTRACT FROM AUTHOR]

With the booming of multi-agent systems (MASs), it is critical for the MASs to tackle the problems arising from the actuator faults, which could result in the MASs suffering from poor performance or even a severe crash. Thus, this article considers an issue of containment control for non-linear MASs with nonautonomous leaders in the presence of actuator faults. A distributed adaptive fault-tolerant containment control via a hierarchical event-triggered scheme is designed to eliminate the adverse effects caused by the additive and multiplicative actuator faults on the systems. Correspondingly, two kinds of triggering functions for followers and nonautonomous leaders are constructed, respectively. It is worth noting that the related thresholds of triggering functions can be dynamically adjusted due to the adaptive auxiliary parameters, by which fewer triggering instants are needed. By utilizing adaptive strategies, the self-regulation of fault-tolerant containment control via a hierarchical event-triggered scheme is improved. After that, a sufficient condition is derived from making the MASs stabilizable. In addition, the proof of eliminating Zeno behavior is given. The experimental results demonstrate the validity of these theoretical findings exhaustively. [ABSTRACT FROM AUTHOR]

An issue of actuator faults in non-linear multi-agent systems with multiple leaders is addressed in this work. Through an event-triggered mechanism, a novel fault-tolerant containment control protocol is designed to eliminate the adverse effects of actuator faults on the systems, and the communication resources can be saved efficiently in the meantime. The self-regulation of the event-triggered mechanism is enhanced significantly by utilizing the adaptive updating strategies, and the proposed triggering thresholds are both time-dependent and state-dependent. A sufficient condition is derived to make the systems with aperiodic sampling stabilizable. Moreover, it is proved that Zeno behavior can be avoided in this article. A numerical simulation is also presented to exhaustively illustrate the effectiveness of the designed scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the output regulation problem of the nonlinear multi-agent systems based on dynamic neural networks. Assume that the models of following agents in the considered systems are unknown, and the state of the leader agent is not completely measurable for each follower. By employing Lyapunov approach, a dynamic neural network is established to approximate the systems of the following agents. Based on the dynamic neural network, a state feedback control law is designed guaranteeing the following agents can asymptotically track the reference generated by an exosystem. The exosystem is regarded as the active leaders in the multi-agent systems. A numerical simulation example is provided to demonstrate the effectiveness of the obtained results. [Copyright &y& Elsevier]