In this paper, we study the robust consensus problem for a group of linear discrete-time or continuous-time agents to coordinate over an uncertain communication network, which is to achieve consensus ...against transmission errors and noises. We model the network by communication links subject to deterministic uncertainties, which can be additive perturbations described by either some unknown transfer functions or norm bounded matrices. We show that the robust consensus problem can generally be solved by solving a simultaneous H ∞ control problem for a set of low-dimensional subsystems. We also derive necessary conditions for the existence of a protocol achieving robust consensus. The results show that for discrete-time agents the uncertainty size must not exceed the inverse of the Mahler measure of the agents, while for continuous-time agents it must be less than the unity. Sufficient conditions in terms of linear matrix inequalities are further presented to design the robust consensus protocols.
This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design ...consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this technical note, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.
This technical brief considers the distributed consensus problems for multi-agent systems with general linear and Lipschitz nonlinear dynamics. Distributed relative-state consensus protocols with an ...adaptive law for adjusting the coupling weights between neighboring agents are designed for both the linear and nonlinear cases, under which consensus is reached for all undirected connected communication graphs. Extensions to the case with a leader-follower communication graph are further studied. In contrast to the existing results in the literature, the adaptive consensus protocols here can be implemented by each agent in a fully distributed fashion without using any global information.
This technical note considers the distributed tracking control problem of multiagent systems with general linear dynamics and a leader whose control input is nonzero and not available to any ...follower. Based on the relative states of neighboring agents, two distributed discontinuous controllers with, respectively, static and adaptive coupling gains, are designed for each follower to ensure that the states of the followers converge to the state of the leader, if the interaction graph among the followers is undirected, the leader has directed paths to all followers, and the leader's control input is bounded. A sufficient condition for the existence of the distributed controllers is that each agent is stabilizable. Simulation examples are given to illustrate the theoretical results.
This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown ...control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, based on the local state information of neighboring agents, a fully distributed continuous adaptive consensus protocol is designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set. For the case where there exists a leader whose control input is unknown and bounded, a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.
This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics for both the cases without and with a leader whose control input might be ...nonzero and time varying. For the case without a leader, based on the relative output information of neighboring agents, two types of distributed adaptive dynamic consensus protocols are proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication graph and the node-based adaptive protocol which uses a time-varying coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for all undirected connected communication graphs. It is shown that the edge-based adaptive consensus protocol is applicable to arbitrary switching connected graphs. For the case where there exists a leader whose control input is possibly nonzero and bounded, a distributed continuous adaptive protocol is designed to guarantee the ultimate boundedness of the consensus error with respect to any communication graph which contains a directed spanning tree with the leader as the root and whose subgraph associated with the followers is undirected, requiring neither global information of the communication graph nor the upper bound of the leader’s control input. A distributed discontinuous protocol is also discussed as a special case. Simulation examples are finally given to illustrate the theoretical results.
This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus ...protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.
This paper studies both continuous and discrete time consensus problems for multi-agent systems with linear time-invariant agent dynamics over randomly switching topologies. The switching is governed ...by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. Necessary and sufficient conditions are derived for achieving consensus under a common control protocol, respectively. It is shown that the effect of switching topologies on consensus is determined by the union of topologies associated with the positive recurrent states of the Markov process. Moreover, the effect of random link failures on discrete time consensus is investigated. The implications and relationships with the existing results are discussed. Finally, the theoretical results are validated via simulations.
This paper investigates the cooperative output regulation problem of heterogeneous linear multi-agent systems over directed graphs with the constraint of communication bandwidth. Given that there ...exists an exosystem whose state information is not available to all agents, the authors develop distributed adaptive event-triggered observers for the followers based on relative information between neighboring agents. It should be pointed out that, two kinds of time-varying gains are introduced to avoid relying on any global information associated with the network, and dynamic triggering conditions are designed to get rid of continuous communications. On the basis of the designed observers, the authors devise a local controller for each agent. Compared with the existing related works, the main contribution of the current paper is that the cooperative output regulation problem for general directed graphs is solved requiring neither global information nor continuous communications.
This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with ...existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader's dynamics may be different with those of the followers' dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader's output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.
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