Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.     

Output consensus for heterogeneous multiagent systems with Markovian switching network topologies

This paper investigates the output consensus problem of heterogeneous continuous‐time multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time‐homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel dynamic consensus controller is proposed. The controller gains are designed based on the information of the expectation graph and the solutions to regulator equations. Furthermore, a necessary and sufficient condition is presented for output consensus of the controlled multiagent system in mean square sense. Finally, a simulation example is provided to corroborate the effectiveness of the proposed controller.     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Adaptive mean-square consensus of heterogeneous multiagent systems with stochastic switching topologies

The leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous-time discrete-state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example.     

Disturbance observer–based consensus tracking for nonlinear multiagent systems with switching topologies

This paper considers the leader‐follower consensus tracking problem for nonlinear multiagent systems with external disturbances and switching topologies. A distributed disturbance observer is constructed to estimate the disturbances suffered by the followers. Then, a distributed consensus protocol is proposed for the consensus tracking problem with disturbance rejection under a fixed directed topology based on the disturbance observer. Next, this result is extended to the case in which the switching communication topology only frequently but not always contains a directed spanning tree. By selecting the parameters appropriately such that the communication time satisfies various preset conditions, it is theoretically proven that the consensus tracking with disturbance rejection can also be achieved by the multiagent systems. Finally, a simulation example is presented to demonstrate the performance of the proposed control scheme.     

Output sign‐consensus of heterogeneous multiagent systems over fixed and switching signed graphs

This paper investigates output sign‐consensus of multiagent systems over directed signed graphs. In signed graphs, the sign of each edge stands for either hostile interaction (associated with positive sign) or antagonistic interactions (associated with negative sign) among agents. Agent dynamics are heterogeneous, allowing coexistence of distinct agent dynamics in one group. Heterogeneity in this paper also implies that the states of different agents may have different dimensions, but their outputs should have the same dimension. Distributed control laws are designed for both fixed and switching graph topologies. For fixed topology, the graph is assumed to be eventually positive. For switching topology, the graph needs to be jointly eventually positive, which extends the well‐known concept of joint connectivity by taking dwell time into consideration.     

Sampled‐data consensus of multiagent systems with switching jointly connected topologies via time‐varying Lyapunov function approach

Consensus problem of multiagent systems with switching jointly connected topologies under sampled‐data control is studied in this article. The main contribution is that the consensus problem for such system is solved without the assumption that the system matrices are stable or critically stable. For this purpose, a time‐varying Lyapunov function method is utilized to describe the state characteristics with switching jointly connected topologies. Based on the time‐varying matrix of Lyapunov function, the “decline” characteristics at the switching instants is derived to compensate the divergence among the agents with disconnected topologies. Utilizing the “decline” characteristics, the overall consensus of such system can be guaranteed in the framework of dwell time. Finally, the effectiveness of the proposed result is illustrated by two numerical examples.     

Guaranteed‐performance consensus tracking of singular multiagent systems with Lipschitz nonlinear dynamics and switching topologies

In this paper, the problem of guaranteed‐performance consensus tracking of continuous‐time singular multiagent systems with Lipschitz nonlinearities and switching topologies is investigated. Consideration is that the interaction of the concerned agent network is described by a set of directed graphs with the union graph having a directed spanning tree rooted at the leader. To establish the guaranteed‐performance criterion, a quadratic performance function is constructed by utilizing the consensus errors among all agents. Then, a consensus protocol that collects the local information from neighboring agents is proposed to achieve consensus tracking and to guarantee the consensus regulation performance of the multiagent systems. On the basis of nonsingular transformation approach, singular systems theory, and Lyapunov stability analysis, the concerned guaranteed‐performance consensus tracking problem is cast into the admissibility analysis for an equivalent kind of switched singular consensus error system. Furthermore, sufficient conditions on the guaranteed‐performance consensus tracking protocol design are formulated in terms of linear matrix inequalities. Finally, numerical examples are employed to demonstrate the effectiveness of the theoretical results.     

Distributed adaptive integral‐type event‐triggered cooperative output regulation of switched multiagent systems by agent‐dependent switching with dwell time

This article presents a distributed adaptive integral‐type event‐triggered scheme (ETS) and an agent‐dependent switching strategy with dwell time to solve the cooperative output regulation problem for switched multiagent systems. First, by constructing an adaptive law to dynamically update the time‐varying coupling weights for all the communication links, a fully distributed ETS is designed, where only the local information of the topology is adopted. Based on the integral‐type triggering condition, the interevent interval is substantially enlarged and Zeno behavior is explicitly ruled out. Second, each agent permits all the subsystems to be unstabilizable. The switching signal for each agent is different, and any adjacent switches of each agent satisfy the preset dwell time. Under the designed switching strategy, the solvability of the regulation problem is guaranteed. Finally, the effectiveness of the designed ETS and switching strategy is substantiated by an example.     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.     

Event‐triggered distributed constrained consensus

We consider a distributed consensus problem for continuous‐time multi‐agent systems with set constraints on the final states. To save communication costs, an event‐triggered communication‐based protocol is proposed. By comparing its own instantaneous state with the one previously broadcasted to neighbours, each agent determines the next communication time. Based on this event‐triggered communication, each agent is not required to continuously monitor its neighbours' state and the communication only happens at discrete time instants. We show that, under some mild conditions, the constrained consensus of the multi‐agent system with the proposed protocol can be achieved with an exponential convergence rate. A lower bound of the transmission time intervals is provided that can be adjusted by choosing different values of parameters. Numerical examples illustrate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered output synchronization of heterogeneous multi‐agent systems

This paper proposes a control architecture that employs event‐triggered control techniques to achieve output synchronization of a group of heterogeneous linear time‐invariant agents. We associate with each agent an event‐triggered output regulation controller and an event‐triggered reference generator. The event‐triggered output regulation controller is designed such that the regulated output of the agent approximately tracks a reference signal provided by the reference generator in the presence of unknown disturbances. The event‐triggered reference generator is responsible for synchronizing its internal state across all agents by exchanging information through a communication network linking the agents. We first address the output regulation problem for a single agent where we analyze two event‐triggered scenarios. In the first one, the output and input event detectors operate synchronously, meaning that resets are made at the same time instants, while in the second one, they operate asynchronously and independently of each other. It is shown that the tracking error is globally bounded for all bounded reference trajectories and all bounded disturbances. We then merge the results on event‐triggered output regulation with previous results on event‐triggered communication protocols for synchronization of the reference generators to demonstrate that the regulated output of each agent converges to and remains in a neighborhood of the desired reference trajectory and that the closed‐loop system does not exhibit Zeno solutions. Several examples are provided to illustrate the advantages and issues of every component of the proposed control architecture. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

Formation control of singular multiagent systems with switching topologies

This paper is concerned with the time‐varying formation control problem for singular multiagent systems with switching topologies. First, in order to eliminate the pulse solution of singular systems and extend the formation function set, the distributed formation controller has been formulated based on the output information of the agents. Then, the explicit expression of formation position function is presented based on the impulse free and the equivalent transformation of singular multiagent systems. Next, the sufficient and necessary conditions of the feasibility of the formation function are provided. Moreover, the sufficient conditions of formation control of singular multiagent systems with switching topologies are presented and the algorithm is designed to solve the distributed controller. Finally, the validity of the proposed approaches is verified by numerical simulation in this paper.     

Observer‐based consensus control of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks

This article investigates the leader‐following consensus of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks. Unlike the related works, the communication channels considered herein are subjected to successful but recoverable attacks, and when the channels work well, the network topology is time‐varying and described by a semi‐Markovian switching topology. Due to the effect of attacks, the communication network is intermittently paralyzed. For the cases that the transition rates of semi‐Markovian switching topologies are completely known and partially unknown, observer‐based control protocols and sufficient conditions are proposed, respectively, to ensure the consensus of the systems in the mean square sense. Finally, simulation examples are given to illustrate the validity of the theoretical results.     

Containment control of stochastic multiagent systems with semi‐Markovian switching topologies

The containment control of stochastic multiagent systems with semi‐Markov switching topologies is investigated in this paper. The general case that the distribution function of the sojourn time is dependent on both the current system mode and the target mode is considered. Taking state multiplicative noise into account and using stochastic techniques, sufficient conditions to achieve the containment control in the asymptotic mean square sense are obtained in a form of linear matrix inequalities and the controller design condition is given. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.     

Mean square leader-following consensus of heterogeneous multi-agent systems with Markovian switching topologies and communication delays

This article considers the mean square leader-following output consensus problem of heterogeneous multi-agent systems under randomly switching topologies and time-varying communication delays. By modeling the switching topologies as a time-homogeneous Markov process and taking the communication delays into consideration, a distributed observer is proposed to estimate the state of the leader. A novel distributed output feedback controller is then designed. By constructing a novel switching Lyapunov functional, an easily-verifiable sufficient condition to achieve the mean square leader-following output consensus is given. Finally, two simulation examples are presented to show the effectiveness of the proposed control scheme.     

Target controllability of multiagent systems under fixed and switching topologies

In this article, the target controllability of multiagent systems under fixed and switching topologies is investigated, respectively. In the fixed topology setting, some necessary and/or sufficient algebraic and graph‐theoretic conditions are proposed, and the target controllable subspace is quantitatively studied by virtue of almost equitable graph vertex partitions. In the switching topology setting, based on the concepts of the invariant subspace and the target controllable state set, some necessary and sufficient algebraic conditions are obtained. Moreover, the target controllability is studied from the union graph perspective. The results show that when the union graph of all the possible topologies is target controllable, the multiagent system would be target controllable even if each of its subsystems is not. Numerical simulations are provided finally to verify the effectiveness of the theoretical results.     

Robust node‐to‐node consensus of linear multiagent systems with directed switching topologies subject to uncertain pinning communications

This paper is focused on the node‐to‐node consensus problem of multiagent systems consisting of general linear node dynamics under directed switching topologies. Specifically, it is assumed that the multiagent systems under consideration have 2 layers, ie, leader layer and follower layer. When uncertainties on the pinning links between the 2 layers exist, the coordination goal is to present some robust control laws, which are distributed such that the states of each follower asymptotically converge to those of its corresponding leader. By using tools from M‐matrix theory and multiple Lyapunov methods, some sufficient criteria are derived to achieve this goal. Finally, 2 simulation examples are performed to validate the effectiveness of the theoretical results.     

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

This paper focuses on the distributed event‐triggered fixed‐time consensus control problem of leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances. Two distributed fixed‐time consensus protocols are proposed based on distributed event‐triggered strategies, which can substantially reduce energy consumption and the frequency of the controller updates. It is proved that under the proposed distributed event‐triggered consensus tracking control strategies, the Zeno behavior is avoided. Compared with the finite‐time consensus tracking, the fixed‐time consensus tracking can be achieved within a settling time regardless of the initial conditions. Finally, 2 examples are performed to validate the effectiveness of the distributed event‐triggered fixed‐time consensus tracking controllers.