Jinliang Shao

Leader-following formation control for second-order multi-agent systems with time-varying delays

This paper investigates a leader-following formation control problem for second-order multi-agent systems with nonuniform time-varying communication delays under directed topologies. We first propose a consensus protocol and give a sufficient condition for second-order consensus of the system. Then, under a framework of multiple leaders, the protocol is applied to the formation control, including time-invariant formation and time-varying formation as well as time-varying formation for trajectory tracking. It is shown that the agents will attain the desired formation under the protocol. Finally, several simulations are conducted to illustrate the effectiveness of our theoretical results.

A novel analysis on the efficiency of hierarchy among leader-following systems

In a recent NATURE paper, Nagy et al. find a well-defined hierarchy among the individuals of the pigeon flock, which may lead to a rapid decision making in the directional choice dynamics of the flock. Motivated by this interesting discovery, we present a novel analysis on the efficiency of the hierarchical topology among the leader-following systems in this paper. To this end, we first propose a measurement of the convergence rate of leader-following consensus, and then connect the convergence rates with the communication topologies of leader-following systems. It is proved that the hierarchical network organization can achieve the best performance in terms of convergence rates. It is also established that the connections between the leader and the followers have effective impacts on increasing the convergence rates. Extensive numerical results are provided to show the effectiveness of our conclusions.

Group consensus for second-order discrete-time multi-agent systems with time-varying delays under switching topologies

This paper addresses group consensus for multi-agent systems with switching topologies and time-varying delays, where all agents are described by discrete-time second-order dynamics. Based on the relationship between zero/nonzero in-degree graphs and nonnegative matrices group consensus criteria, which is presented in terms of easily checkable graph topology conditions, is obtained for multi-agent systems with time-varying delays under switching topologies. Furthermore, numerical examples are presented to illustrate the obtained results, and the essential of some conditions and assumptions is verified for given switching communication topologies.

Asynchronous containment control for discrete-time second-order multi-agent systems with time-varying delays

Abstract The asynchronous containment control problem of second-order discrete-time multi-agent systems with time-varying delays is investigated. Asynchrony in this paper means that each agent updates state information via its clock that is independent of those of the other agents’, and the time sequence over which each agent updates its state information is not necessarily equispaced. An asynchronous distributed control protocol is designed to realize local control strategies for the second-order discrete-time multi-agent system. By utilizing the proposed protocol and properties of Laplacian matrix, the asynchronous containment control problem of second-order multi-agent systems is equivalently transformed into a stability problem of synchronous error system. Based on the nonnegative matrix theory and graph theory, a necessary and sufficient condition is obtained to make all the followers asymptotically converge to the convex hull formed by the stationary leaders. Finally, some simulation examples are presented for illustration.

Formation Control of Second-Order Multiagent Systems with Time-Varying Delays

A formation control problem for second-order multiagent systems with time-varying delays is considered. First, a leader-following consensus protocol is proposed for theoretical preparation. With the help of Lyapunov-Krasovskii functional, a sufficient condition under this protocol is derived for stability of the multiagent systems. Then, the protocol is extended to the formation control based on a multiple leaders’ architecture. It is shown that the agents will attain the expected formation. Finally, some simulations are provided to demonstrate the effectiveness of our theoretical results.

Second-Order Leader-Following Consensus of Multiagent Systems with Time Delays

This paper is concerned with a leader-following consensus problem of second-order multiagent systems with a constant acceleration leader and time-varying delays. At first, a distributed control protocol for every agent to track the leader is proposed; then by utilizing the Lyapunov-Razumikhin function, the convergence analysis under both fixed and switching interconnection topologies is investigated. For the case of fixed topology, a sufficient and necessary condition is obtained, and for the case of switching topology, a sufficient condition is derived under some assumptions. Finally, simulation examples are provided to demonstrate the effectiveness of the theoretical results.

Event-triggered containment control for second-order multi-agent systems with sampled position data

This paper is concerned with the problem of event-triggered containment control for second-order multi-agent systems with sampled position data. First, a distributed event-triggered containment control protocol is designed, which utilizes the sampled position data only and allows the event-triggering condition to be intermittently examined at constant sampling instants. Then, based on the algebraic graph theory and matrix theory, a sufficient condition on the communication topology, the controller gains, and the sampling period is derived so as to achieve containment control. Finally, a numerical example is provided to verify the theoretical results.

Couple-group consensus for second-order multi-agent systems with the effect of second-order neighbours’ information

This paper investigates a couple-group consensus problem of second-order multi-agent systems with the impact of second-order neighbours’ information. For systems with/without time delays, couple-group consensus criteria are established in the form of linear matrix inequalities by utilizing both model transformation and stability theories. The main results indicate that the group consensus for multi-agent systems under the effect of second-order neighbours’ information can be achieved based on the premise of a generalized balanced couple. Finally, illustrative examples are presented to demonstrate the effectiveness of the theoretical results.

Asynchronous group consensus for discrete-time heterogeneous multi-agent systems under dynamically changing interaction topologies

Abstract This paper aims to investigate the asynchronous group consensus problem for discrete-time heterogeneous multi-agent systems under dynamically changing interaction topologies. Here the heterogeneous system is composed of hybrid dynamic agents including first-order dynamic agents and second-order dynamic agents, and asynchrony implies that each agent only detects the neighbors’ state information at certain discrete time instants determined by its own clock that is independent of the other agents’. For different kinds of agents, two asynchronous consensus protocols are proposed to realize local control strategies, respectively. With the help of nonnegative matrix theory, in particular the product properties of row-stochastic matrices from a noncompact set, a sufficient condition in terms of the interaction topologies is established to guarantee that the asynchronous group consensus problem can be solved under very relaxed conditions, i.e., the union of the effective interaction topologies across any time intervals with some given length is only required to contain a spanning tree. Numerical examples are finally provided to validate the theoretical results.

Containment control for heterogeneous multi-agent systems with asynchronous updates

Abstract This paper is concerned with the asynchronous containment control problem for heterogeneous multi-agent systems with time-varying delays. Here, asynchrony means that each agent updates the state information by its own clock that is independent of the other agents’ update times, and the update intervals of each agent are not necessarily equispaced. It is assumed that the leaders are stationary, and the followers can be classified into two generic categories: the followers with the first-order dynamics and the followers with second-order dynamics. For different kinds of followers, two distributed containment control protocols are presented to guarantee that all the followers can asymptotically converge into the convex hull formed by the leaders. The properties of the product of infinite nonnegative matrices are explored to arrive at that the asynchronous containment control can be achieved under the proposed protocols if and only if the communication topology among the agents contains a directed spanning forest rooted at the leaders. At last, simulation results are given to demonstrate the validity of the theoretical findings.