Heterogeneous Linear Multi-agent Systems Research Articles

Distributed Optimization of Uncertain Multiagent Systems With Disturbances and Actuator Faults via Exosystem Observer-Based Output Regulation

This paper investigates a distributed optimization problem for heterogeneous linear multi-agent systems with uncertain parameters and external disturbances. For each agent, the optimal solution of the global objective functions can be regarded as an unknown constant reference signal. From this angle, the problem is transformed into an output regulation problem for an exosystem whose states and outputs are to be estimated. To ensure the trackability of the estimated signal, a fundamental design condition for the exosystem observer to achieve robust output regulation is given in the context of internal model control. Exact global optimization is then realized by embedding an appropriate distributed optimization algorithm (i.e., the exosystem observer) in each agent to estimate the global optimal solution. The result for exosystem observer design is extended to yield an adaptive fault-tolerant control algorithm to deal with a class of practical actuator fault uncertainties. The exosystem observer-based output regulation method provides a general distributed robust optimization framework for uncertain systems with disturbances and actuator faults, which can directly apply to various consensus problems. Simulations are provided to illustrate the effectiveness of the method.

Resilient time‐varying output formation tracking of heterogeneous linear multiagent systems under malicious false data injection attacks and denial‐of‐service attacks over digraphs

AbstractA distributed control fashion of cooperative formation tracking may be vulnerable to malicious attacks on sensors and communications that deteriorate the formation tracking performance or even destabilize the entire multiagent system. This article addresses a resilient time‐varying output formation tracking problem of linear heterogeneous multiagent systems, where an attacker can adversely inject false data injection (FDI) attacks on sensors and Denial‐of‐Service (DoS) attacks on communications. Both characteristics will not only enhance the practical relevance of the studied issue, but also bring nontrivial design challenges of distributed control algorithms and convergence analysis. A novel resilient distributed control architecture is developed to guarantee a global exponential time‐varying output formation tracking. In particular, the design includes features: (1) a resilient distributed leader estimator is developed to estimate the leader's state for each follower under DoS attacks over digraphs; (2) a distributed output feedback controller integrated with an observer‐based resilient mechanism is developed to achieve the time‐varying output formation tracking under attacks; (3) unlike existing related works to handle attacks as bounded disturbances or faults, the proposed design is resilient to enable exponential convergence, whereas many related works obtain uniformly ultimately boundedness (UUB) convergence. Simulation results are presented to validate the design's effectiveness.

A fully distributed adaptive event-triggered control for output regulation of multi-agent systems with directed network

This paper considers the cooperative output regulation problem for heterogeneous linear multi-agent systems via an event-triggered control strategy for the directed graph. First, to cancel the requirement of continuous update of the control rule, a novel distributed event-triggered control protocol such that each agent can determine when to update the control rule asynchronously, where the Zeno behavior is strictly ruled out based on the contradiction. Later, to make the multi-agent systems more flexible, based on the adaptive control technology, the cooperative output regulation problem of heterogeneous linear multi-agent systems can be solved in a fully distributed manner, where the global information, such as the number of agents or the eigenvalues of Laplacian matrix, is no longer needed. Furthermore, the considered communication network is a more general directed network, in which the minimum communication channel of the directed network is halved compared with the undirected case. Finally, the effectiveness of the proposed control strategy is verified on a group of heterogeneous agents.

Output Consensus Problem for Linear Heterogeneous Multiagent Systems With Dynamic Event-Based Impulsive Control

This article has a research on the problem of output consensus for linear heterogeneous multiagent systems (LHMASs) by using dynamic event-based impulsive control. First, according to whether the transfer of information from different agents is continuous or not, two corresponding control approaches are provided, respectively. Second, for the case of continuous information transfer, the corresponding dynamic event-triggered condition is obtained. Third, for the case that the information communication from each agent only occurs at the event-triggered time instant, two different dynamic event-triggered conditions according to whether the event-triggered time instant for each agent is same or not are proposed, respectively. For all these event-triggered mechanisms, both the output consensus conditions and the proofs of avoiding Zeno-behavior are given. Moreover, the effect of the dynamic variables belong to these dynamic event-triggered conditions on the minimum event-triggered time interval is also discussed. Finally, the analysis for a numerical example with two control approaches and the corresponding event-triggered conditions provided in this article is obtained to support our opinions.

Adaptively Distributed Nash Equilibrium Seeking of Noncooperative Games for Uncertain Heterogeneous Linear Multi-Agent Systems

This paper presents the design of adaptively distributed Nash Equilibrium (NE) seeking algorithms in noncooperative games for heterogeneous general linear multi-agent systems (MASs) under unknown unmodeled dynamics and bounded disturbances. Different from existing works that only consider single or multiple integrators, we aim to steer agents' outputs of MASs with nonidentical dynamics to the NE in a distributed way and not needing known information on the Lipschitz and monotone constants of pseudo-gradients as well as the algebraic connectivity of the graph. To overcome difficulties brought by heterogeneous dynamics and NE seeking requirements, we first present an adaptively distributed NE seeking algorithm that can tune on-line the edges of graphs to solve the studied problem. By leveraging monotone and matrix properties, the global asymptotic convergence to the NE is obtained. Moreover, this design is extended to develop another adaptively distributed NE seeking algorithm to tackle the impact of unknown dynamics and disturbances. Two exam -ples with numerical simulation results are provided to illustrate the effectiveness of the developed NE seeking algorithms.

Adaptive Bipartite Output Tracking Consensus in Switching Networks of Heterogeneous Linear Multiagent Systems Based on Edge Events.

This article focuses on the problem of adaptive bipartite output tracking for a class of heterogeneous linear multiagent systems (MASs) by asynchronous edge-event-triggered communications under jointly connected signed topologies. By designing the observers to estimate the states of followers and the dynamic compensators to estimate the states of zero input and nonzero input leader, respectively, the fully distributed edge-event-triggered control protocol is presented. Moreover, it is proven that the bipartite output tracking problem is implemented, and the systems do not exhibit Zeno behavior under a fully distributed control strategy with edge-event-triggered mechanisms. Compared with the existing works, one of the highlights of this article is the design of triggering mechanisms, under which the leader avoids continuous information transmission and any pair of followers that make up the edge asynchronously transmit information through the edge. The methods greatly avoid unnecessary information transmission in the systems. Finally, several simulation examples are introduced to demonstrate the theoretical results obtained in this article.

Bipartite fixed-time output containment control of heterogeneous linear multi-agent systems

<abstract><p>This study researches the bipartite fixed-time output containment control problem of heterogeneous linear MASs with signed digraphs. The leaders' states can be estimated by a designed distributed bipartite compensator. Furthermore, each follower is allocated a time-varying coupling weight, an adaptive bipartite fixed-time protocol is raised which can estimate the leader's system matrix but also the leader's state. On the foundation of control protocols, followers' outputs are included by the convex hull constituted by leaders' outputs. In addition, by utilizing the Lyapunov function theory, some abundant speculative knowledges are deduced to guarantee adaptive bipartite fixed-time output containment of multi-agent systems. Finally, the feasibility of the anticipant theoretical results is verified by a set of simulation examples.</p></abstract>

Attack-Resilient Distributed Convex Optimization of Cyber–Physical Systems Against Malicious Cyber-Attacks Over Random Digraphs

This article addresses a resilient exponential distributed convex optimization problem for a heterogeneous linear multiagent system under Denial-of-Service (DoS) attacks over random digraphs. The random digraphs are caused by unreliable networks and the DoS attacks, allowed to occur aperiodically, refer to an interruption of the communication channels carried out by the intelligent adversaries. In contrast to many existing distributed convex optimization works over a perfect communication network, the global optimal solution might not be sought under the adverse influences that result in performance degradations or even failures of optimization algorithms. The aforementioned setting poses certain technical challenges to optimization algorithm design and exponential convergence analysis. In this work, several resilient algorithms are presented such that a team of agents minimizes a sum of local nonquadratic cost functions in a safe and reliable manner with the global exponential convergence. Numerical simulation results are further presented to validate the effectiveness of the proposed distributed approaches.

Cooperative Output Feedback Tracking Control of Stochastic Linear Heterogeneous Multiagent Systems

We study cooperative output feedback tracking control of stochastic linear heterogeneous leader- following multiagent systems. Each agent has a conti- nuous-time linear heterogeneous dynamics with incompletely measurable state, and there are additive and multiplicative noises along with information exchange among agents. We propose a set of admissible distributed observation strategies for estimating the leader’s and the followers’ states and a set of admissible cooperative output feedback control strategies based on the certainty equivalence principle. By output regulation theory and stochastic analysis, we show that for observable leader’s dynamics and stabilizable and detectable followers’ dynamics, if the intensity coefficient of multiplicative noises multiplied by the sum of real parts of the leader’s unstable modes is less than one-fourth of the minimum nonzero eigenvalue of graph Laplacian, then there exist admissible distributed observation and cooperative control strategies to ensure mean square bounded output tracking, provided the associated output regulation equations are solvable. Finally, the effectiveness of our control strategies is demonstrated by a numerical simulation.

Distributed Event-Triggered Output Consensus for General Linear Heterogeneous Multi-Agent Systems With System Uncertainties

Distributed Event-Triggered Output Consensus for General Linear Heterogeneous Multi-Agent Systems With System Uncertainties

Distributed output-feedback resilient fault-tolerant tracking control of uncertain heterogeneous linear MASs under directed topologies and DoS attacks

This paper presents a distributed output-feedback resilient tracking fault-tolerant control (FTC) protocol for uncertain heterogeneous linear multi-agent systems (MASs) with directed topologies and DoS attacks. The uncertainty, actuator fault and nonidenticality in agents and DoS attacks in directed communication topologies, make it a challenging task to achieve distributed output-feedback FTC objective. In order to solve this difficulty, a hierarchical framework is introduced. The basic idea is to design distributed resilient observers under directed topologies and DoS attacks. By virtue of switching systems theory, the upper bounds of attack frequency and attack duration are obtained. Based on neural networks approximation technique and model reference tracking method, a novel output-feedback FTC scheme is proposed. Lastly, simulation example indicates the validity of the proposed method.

Leader-Following Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays via Adaptive Distributed Observers.

This article investigates the leader-following consensus problem of heterogeneous linear multiagent systems under switching and directed topologies. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established with which the main results of this article can be obtained. An adaptive distributed observer, taking into consideration of communication time delays, is proposed for each follower to estimate the leader's system matrices and its state. Then, a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multiagent system achieves the leader-following output consensus. Two examples are finally given to illustrate the effectiveness of the proposed controller.

Distributed Optimal Coordination for Heterogeneous Linear Multiagent Systems

This article studies the problem of distributed optimal coordination (DOC) for heterogeneous linear multiagent systems. Compared with the existing results where the structure constraints on local gradients or system matrices are required, the considered DOC framework is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sufficiently general</i> in the sense that no extra assumption is required except for the convexity/differentiability of local objective functions and the controllability/observability of linear systems. A necessary and sufficient condition for the existence of the solution to the DOC problem is derived in terms of the relationship between the objective function and so-called steady-state reachable set of linear systems. Under this fundamental condition, the original DOC problem is transformed into the one with additive equality constraint, without loss of the optimality, which generates a trackable solution for agent dynamics. By using a new state transformation technique, it is proved that the proposed DOC algorithm guarantees the global asymptotical convergence by utilizing only local interaction. Simulation results on the motion coordination illustrate the proposed algorithm.

Distributed Adaptive Finite-Time Bipartite Containment Control of Linear Multi-Agent Systems

Predefined the problem of finite-time bipartite containment control for heterogeneous linear multi-agent systems under directed topokogy. By designing a distributed bipartite compensator, the problem of bipartite containment can be considered as the problem of cooperative output regulation. Adaptive protocols are put forward by allocating a time-varying coupling weight to each follower. We thereby raise the distributed dynamic state feedback protocols combined with adaptive control, by which followers are driven to move to convex hull spanned by leaders in finite time. Furthermore, by employing the method of Lyapunov function, some plentitude criteria are inferred to pledge adaptive finite-time bipartite containment of heterogeneous agents. The final simulation examples proof the feasibility of the desired theoretical results.

Adaptive fault-tolerant control of heterogeneous MASs based on dynamic event-triggered communication

This paper describes a solution to the problem of fault-tolerant control (FTC) problem for leader-following heterogeneous linear multi-agent systems (MASs) subject to loss of effectiveness and time-varying additive actuator faults. The main goal of the proposed FTC approach is to maintain the behaviour of the heterogeneous MASs in spite of actuator faults and to save on bandwidth required for the MASs communication by using a dynamic event-triggered communication mechanism. Firstly, a fault estimation observer, which deals with linear systems with matched disturbances, is constructed to estimate simultaneously the actuator faults and the followers' states. Then, an FTC with dynamic event-triggered communication is proposed. The latter is based on a dynamic internal reference for each agent and exploits the estimated faults. Thus, it is at first shown that the FTC problem can be indirectly solved through the consensus tracking of the defined internal references. Then, a sufficient condition of consensus tracking for the internal references with a dynamic event-triggered communication is proposed. Finally, a sufficient and necessary condition is derived for the FTC of linear heterogeneous multi-agent systems. The effectiveness of the proposed approach is illustrated with a numerical simulation.

Event-triggered [formula omitted] output consensus of heterogeneous linear multi-agent systems

This paper addresses the leader-following H∞ output consensus problem of heterogeneous linear multi-agent systems (MASs) under directed graphs. Both state feedback and output feedback based event-triggered control (ETC) protocols are developed. First, to avoid continuous communication between neighboring agents, the open-loop estimation method is used in the proposed ETC protocols. Second, a unified time- and event-triggering mechanism with an explicit minimum inter-event time (MIET) is further developed based on the open-loop estimation method so that Zeno behavior can be excluded. It is shown that under the proposed ETC protocols, the controlled MAS can achieve H∞ output consensus. Finally, two numerical examples are provided to verify effectiveness of the proposed ETC protocols.

Adaptive Bipartite Fixed-Time Time-Varying Output Formation-Containment Tracking of Heterogeneous Linear Multiagent Systems.

This study investigates the bipartite fixed-time time-varying output formation-containment tracking issue for heterogeneous linear multiagent systems with multiple leaders. Both cooperative communication and antagonistic communication between neighbor agents are taken into account. First, the bipartite fixed-time compensator is put forward to estimate the convex hull of leaders' states. Different from the existing techniques, the proposed compensator has the following three highlights: 1) it is continuous without involving the sign function, and thus, the chattering phenomenon can be avoided; 2) its estimation can be achieved within a fixed time; and 3) the communication between neighbors can not only be cooperative but also be antagonistic. Note that the proposed compensator is dependent on the global information of network topology. To deal with this issue, the fully distributed adaptive bipartite fixed-time compensator is further proposed. It can estimate not only the convex hull of leaders' states but also the leaders' system matrices. Based on the proposed compensators, the distributed controllers are then developed such that the bipartite time-varying output formation-containment tracking can be achieved within a fixed time. Finally, two examples are given to illustrate the feasibility of the main theoretical findings.

Fully Distributed Dual-Terminal Event-Triggered Bipartite Output Containment Control of Heterogeneous Systems Under Actuator Faults

This article deals with the fully distributed dual-terminal dynamic event-triggered bipartite output containment control of heterogeneous linear multiagent systems (HLMASs) subject to actuator faults. First, a class of fully distributed dynamic event-triggered observers is proposed over the directed signed communication network for each follower to estimate the leaders’ system matrices and (symmetric) combination states, which are merely available to a small fraction of followers. Then, based on the estimations of leaders’ system matrices, adaptive algorithms are employed to solve the regulator equations. Furthermore, the fully distributed observer-based dynamic event-triggered controllers are proposed by integrating the adaptive gains to compensate for actuator faults. Dual-terminal dynamic event-triggered mechanisms (ETMs) are addressed to exclude not only continuous control updates but also continuous communication among agents. Correspondingly, some mild criteria and the rigorous proofs are established to ensure the implementation of bipartite output containment through the Lyapunov stability theory. Moreover, the strictly positive lower bounds of intervals between two adjacent event-triggered time instants are derived, which indicates that Zeno behavior is ruled out in the dual-terminal dynamic ETMs. Finally, numerical simulations are performed to demonstrate the theoretical analysis.

Energy-Management Strategy of Battery Energy Storage Systems in DC Microgrids: A Distributed Dynamic Event-Triggered H ∞ Consensus Control

Distributed renewable energy source is an advisable solution for dc microgrids to reduce fuel consumption and CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emission. In such microgrids, the installation of two or more battery energy storage (BES) units is utilized to compensate the power imbalance between the sources and loads. Nevertheless, energy management with numerous BES units does not simultaneously consider the impacts of distributed generators (DGs) and constant power loads (CPLs). Since the inaccurate current sharing will shorten the lifetime of the batteries and cause instability problem, this article proposes a distributed secondary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus approach based on the dynamic event-triggered communication method to realize accurate current sharing and efficient operation in the presence of numerous DGs and CPLs. First, the whole state-space function model of the dc microgrid consisting of DGs, batteries, resistive loads, and CPLs, is first built in detail. This model is further transformed into standard linear heterogeneous multiagent systems, which provides an indispensable preprocessing for advanced control strategy application. Then, the distributed secondary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus approach based on the foresaid systems is designed to achieve accurate current sharing. For reducing the communication among batteries and the controller updating frequency, the dynamic event-triggered communication method is proposed. Compared with existing event-triggered methods, the communication and controller updating frequency of the proposed dynamic event-triggered method have been reduced a lot. Additionally, the proposed method can not only avoid the Zeno behavior, but also obtain the lowest bound of the sampled time interval. Finally, the numerical simulation results and experimental results verify the effectiveness of the proposed control strategy.

Leader-Following Almost Output Consensus for Linear Heterogeneous Multiagent Systems With Disturbance-Affected Unstable Zero Dynamics by Output Feedback

A novel design of observer-based output feedback consensus protocols in a low-and-high gain feedback framework is proposed for a linear heterogeneous multiagent system, where the unstable zero dynamics of the follower agents is affected by disturbances. Conditions on the graph that represents the connectivity among the agents and on how the disturbances enter the zero dynamics of the follower agents are identified, under which the leader-following almost output consensus can be attained with the proposed protocols. More specifically, the proposed protocols achieve leader-following output consensus to an arbitrarily high level of accuracy, and the effect of the disturbances on the consensus errors is attenuated to an arbitrarily low level.