Guanghui Wen

Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies

Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.

Designing Fully Distributed Consensus Protocols for Linear Multi-Agent Systems With Directed Graphs

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.

Consensus tracking for higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs

Abstract This paper studies the distributed consensus tracking problem of linear higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs. In this framework, the underlying topology of dynamic agents may switch among several directed graphs, each having a directed spanning tree rooted at the leader. Furthermore, the control inputs to the followers may be temporally missed due to actuator failures and network-induced packet loss. To guarantee asymptotic consensus tracking in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing a switching Lyapunov function and using tools from the M -matrix theory, some sufficient conditions for achieving distributed consensus tracking are provided. Finally, some numerical simulations are given to illustrate the theoretical analysis.

Distributed finite-time tracking control for multi-agent systems: An observer-based approach

Abstract This paper addresses the distributed finite-time tracking control problem for second-order multi-agent systems. First, we propose a finite-time tracking protocol for multi-agent systems by using state feedback. Then, a new class of observer-based control algorithms are designed for achieving finite-time consensus tracking in multi-agent systems with a single active leader, where each agent can only share its position states with its neighbors. Within the same context, the present control algorithms are then extended to solve the finite-time containment tracking problem for multi-agent systems in the presence of multiple active leaders. It is theoretically shown that the position states of the followers will converge to that of the leader or a convex hull spanned by those of the leaders, respectively, in finite time. Furthermore, the finite-time formation control problem is discussed. The effectiveness of the results is also illustrated by numerical simulations.

Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M-matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.

Containment of Higher-Order Multi-Leader Multi-Agent Systems: A Dynamic Output Approach

This technical note addresses the distributed containment control problem for a linear multi-leader multi-agent system with a directed communication topology. A new class of distributed observer-type containment protocols based only on the relative output measurements of the neighboring agents is proposed, removing the impractical assumption in some of the existing approaches that the observers embedded in the multiple dynamic agents have to share information with their neighbors. Under the mild assumption that, for each follower, there exists at least one leader having a directed path to that follower, some sufficient conditions are derived to guarantee the states of the followers to asymptotically converge to a convex hull formed by those of the dynamic leaders. Finally, some numerical simulations on containment of a multi-vehicle system are given to verify the effectiveness of the theoretical results.

Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by multiple non-identical second-order nonlinear systems. First, a class of distributed finite-time protocols are proposed based on the relative position and relative velocity measurements. By providing a topology-dependent Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded. Then, a new class of observer-based algorithms are designed to solve the finite-time consensus tracking problem without using relative velocity measurements. The main contribution of this paper is that, by computing the value of the Lyapunov function at the initial point, the finite settling time can be theoretically estimated for second-order multi-agent systems with the proposed control protocols. Finally, the effectiveness of the analytical results is illustrated by an application in low-Earth-orbit spacecraft formation flying.

Consensus and its ℒ2-gain performance of multi-agent systems with intermittent information transmissions

This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbours intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite ℒ2-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology. The results are then extended to consensus with prescribed ℒ2-gain performance with a virtual leader where the underlying topology is not necessarily strong connected or contain a directed spanning tree. Numerical simulations are finally provided to verify and visualise the theoretical analysis.

H∞ pinning synchronization of directed networks with aperiodic sampled-data communications

This paper addresses the global H∞ pinning synchronization problem for a class of directed networks with aperiodic sampled-data communications. Important yet challenging issues of how many and which nodes should be pinned for realizing global synchronization in a fixed directed network without external disturbances are first discussed. By using a combined tool from the input-delay approach and free-weighting matrices technique, some sufficient synchronizability conditions are then derived for such networks. Furthermore, a multi-step algorithm is designed to estimate the upper bound of the maximum allowable sampling intervals for achieving synchronization. Theoretical results are then extended to global H∞ pinning synchronization in fixed and switched directed networks with external disturbances, showing that a finite H∞ performance index can be guaranteed under some suitable conditions. Finally, numerical simulations are performed to demonstrate the effectiveness of the analytical results.

Distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances

In this article, distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances is investigated. With the aid of sliding-mode control technique, both the finite-time consensus tracking in the presence of a single leader and the finite-time containment control with multiple leaders are in detail analysed. A distinctive feature of this work is that the communication topology among the followers can be directed. It is shown that the states of the followers can track that of the leader when there exists a single leader, and converge to a convex hull spanned by those of the leaders when there exist multiple leaders, both in finite time. Moreover, the finite convergence time is explicitly presented. Numerical examples are finally given to illustrate the theoretical results.