Consensus of switched multi-agent systems

In this paper, we consider the consensus problem of switched multi-agent system composed of continuous-time and discrete-time subsystems. By combining the classical consensus protocols of continuous-time and discrete-time multi-agent systems, we propose a linear consensus protocol for switched multi-agent system. Based on the graph theory and Lyapunov theory, we prove that the consensus of switched multi-agent system is solvable under arbitrary switching with undirected connected graph, directed graph and switching topologies, respectively. Simulation examples are also provided to demonstrate the effectiveness of the theoretical results.Comment: 16 pages, 4 figure

Minimum-Rank Dynamic Output Consensus Design for Heterogeneous Nonlinear Multi-Agent Systems

In this paper, we propose a new and systematic design framework for output consensus in heterogeneous Multi-Input Multi-Output (MIMO) general nonlinear Multi-Agent Systems (MASs) subjected to directed communication topology. First, the input-output feedback linearization method is utilized assuming that the internal dynamics is Input-to-State Stable (ISS) to obtain linearized subsystems of agents. Consequently, we propose local dynamic controllers for agents such that the linearized subsystems have an identical closed-loop dynamics which has a single pole at the origin whereas other poles are on the open left half complex plane. This allows us to deal with distinct agents having arbitrarily vector relative degrees and to derive rank-$1$ cooperative control inputs for those homogeneous linearized dynamics which results in a minimum rank distributed dynamic consensus controller for the initial nonlinear MAS. Moreover, we prove that the coupling strength in the consensus protocol can be arbitrarily small but positive and hence our consensus design is non-conservative. Next, our design approach is further strengthened by tackling the problem of randomly switching communication topologies among agents where we relax the assumption on the balance of each switched graph and derive a distributed rank-$1$ dynamic consensus controller. Lastly, a numerical example is introduced to illustrate the effectiveness of our proposed framework.Comment: Revised version submitted to IEEE Transactions on Control of Network System

Multi-Agent Distributed Coordination Control: Developments and Directions

In this paper, the recent developments on distributed coordination control, especially the consensus and formation control, are summarized with the graph theory playing a central role, in order to present a cohesive overview of the multi-agent distributed coordination control, together with brief reviews of some closely related issues including rendezvous/alignment, swarming/flocking and containment control.In terms of the consensus problem, the recent results on consensus for the agents with different dynamics from first-order, second-order to high-order linear and nonlinear dynamics, under different communication conditions, such as cases with/without switching communication topology and varying time-delays, are reviewed, in which the algebraic graph theory is very useful in the protocol designs, stability proofs and converging analysis. In terms of the formation control problem, after reviewing the results of the algebraic graph theory employed in the formation control, we mainly pay attention to the developments of the rigid and persistent graphs. With the notions of rigidity and persistence, the formation transformation, splitting and reconstruction can be completed, and consequently the range-based formation control laws are designed with the least required information in order to maintain a formation rigid/persistent. Afterwards, the recent results on rendezvous/alignment, swarming/flocking and containment control, which are very closely related to consensus and formation control, are briefly introduced, in order to present an integrated view of the graph theory used in the coordination control problem. Finally, towards the practical applications, some directions possibly deserving investigation in coordination control are raised as well.Comment: 28 pages, 8 figure

Cluster Synchronization of Coupled Systems with Nonidentical Linear Dynamics

This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly correlated if static couplings are used for all individual systems. In this paper, a dynamic coupling structure, which incorporates a global weighting factor and a vanishing auxiliary control variable, is proposed for each agent and is shown to be a feasible solution. Lower bounds on the global and local weighting factors are derived under the condition that every interaction subgraph associated with each cluster admits a directed spanning tree. The spanning tree requirement is further shown to be a necessary condition when the clusters connect acyclicly with each other. Simulations for two applications, cluster heading alignment of nonidentical ships and cluster phase synchronization of nonidentical harmonic oscillators, illustrate essential parts of the derived theoretical results.Comment: 22 pages, 4 figure

Controllability of Heterogeneous Multi-Agent Networks

The existing results on controllability of multi-agents networks are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous multi-agent networks, where the agents are modeled as two types. One type is that the agents are of the same high-order dynamics, and the interconnection topologies of the information flow in different orders are supposed to be different. It is proved that a heterogeneous-topology network is controllable if and only if the first-order information topology is leader-follower connected, and there exists a Laplacian matrix, which is a linear combination of the Laplacian matrices of each order information, whose corresponding topology is controllable. The other type is that the agents are of generic linear dynamics, and the dynamics are supposed to be heterogeneous. A necessary and sufficient condition for controllability of heterogeneous-dynamic networks is that each agent contains a controllable dynamic part, and the interconnection topology of the network is leader-follower connected. If some dynamics of the agents are not controllable, the controllability between the agents and the whole network is also studied by introducing the concept of eigenvector-uncontrollable. Different illustrative examples are provided to demonstrate the effectiveness of the theoretical results in this paper

Containment control of multi-agent systems with measurement noises

In this paper, containment control of multi-agent systems with measurement noises is studied under directed networks. When the leaders are stationary, a stochastic approximation type protocol is employed to solve the containment control of multi-agent systems. By using stochastic analysis tools and algebraic graph theory, some necessary and sufficient criteria are established to ensure the followers converge to the convex hull spanned by the leaders in the sense of mean square and probability 1. When the leasers are dynamic, a stochastic approximation type protocol with distributed estimators is developed and necessary and sufficient conditions are also obtained for solving the containment control problem. Simulations are provided to illustrate the effectiveness of the theoretical results.Comment: 8 page

Event-Triggered Communication and Control of Networked Systems for Multi-Agent Consensus

This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluation of triggers, and the role of imperfect information. The issues raised in our discussion transcend the specific consensus problem and are indeed characteristic of cooperative algorithms for networked systems that solve other coordination tasks. As our discussion progresses, we make these connections clear, highlighting general challenges and tools to address them widespread in the event-triggered control of networked systems

Fully Distributed Adaptive Output Feedback Protocols for Linear Multi-Agent Systems with Directed Graphs: A Sequential Observer Design Approach

This paper studies output feedback consensus protocol design problems for linear multi-agent systems with directed graphs. We consider both leaderless and leader-follower consensus with a leader whose control input is nonzero and bounded. We propose a novel sequential observer design approach, which makes it possible to design fully distributed adaptive output feedback protocols that the existing methods fail to accomplish. With the sequential observer architecture, we show that leaderless consensus can be achieved for any strongly connected directed graph in a fully distributed manner, whenever the agents are stabilizable and detectable. For the case with a leader of bounded control input, we further present novel distributed adaptive output feedback protocols, which include nonlinear functions to deal with the effect of the leaders's nonzero control input and are able to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root.Comment: 14 pages, 8 figures, submitted for publicatio

Coordinated Output Regulation of Heterogeneous Linear Systems under Switching Topologies

This paper constructs a framework to describe and study the coordinated output regulation problem for multiple heterogeneous linear systems. Each agent is modeled as a general linear multiple-input multiple-output system with an autonomous exosystem which represents the individual offset from the group reference for the agent. The multi-agent system as a whole has a group exogenous state which represents the tracking reference for the whole group. Under the constraints that the group exogenous output is only locally available to each agent and that the agents have only access to their neighbors' information, we propose observer-based feedback controllers to solve the coordinated output regulation problem using output feedback information. A high-gain approach is used and the information interactions are allowed to be switched over a finite set of fixed networks containing both graphs that have a directed spanning tree and graphs that do not. The fundamental relationship between the information interactions, the dwell time, the non-identical dynamics of different agents, and the high-gain parameters is given. Simulations are shown to validate the theoretical results

Consensus with Output Saturations

This paper consider a standard consensus algorithm under output saturations. In the presence of output saturations, global consensus can not be realized due to the existence of stable, unachievable equilibrium points for the consensus. Therefore, this paper investigates necessary and sufficient initial conditions for the achievement of consensus, that is an exact domain of attraction. Specifically, this paper considers singe-integrator agents with both fixed and time-varying undirected graphs, as well as double-integrator agents with fixed undirected graph. Then, we derive that the consensus will be achieved if and only if the average of the initial states (only velocities for double-integrator agents with homogeneous saturation levels for the outputs) is within the minimum saturation level. An extension to the case of fixed directed graph is also provided in which an weighted average is required to be within the minimum saturation limit