High-order Linear Time-invariant Multi-agent Systems Research Articles

Distributed control of linear multiagent systems with global and local objectives

In this paper, we consider distributed control problems for high-order linear time-invariant multiagent systems with not only global but also local objectives over fixed directed communication graph topologies. The former is either leaderless synchronization or synchronization to a leader. Local objectives for a subset of agents, on the other hand, are tasks determined around the global objective by agent-specific exosystems. First, we construct reference models for all agents via two existing synchronization results, introduce two classes of distributed controllers, and define the considered problems. We then solve them by utilizing the converging-input converging-state property for a class of linear systems and the feedforward design methodology from the linear output regulation theory. Finally, numerical examples are presented to demonstrate the problems and the theoretical results.

Distributed Containment Control of Multi-agent Systems with General Linear Dynamics and Time-delays

Containment control problems for high-order linear time-invariant multi-agent systems with fixed communication time-delays are investigated. Based on Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) method, sufcient conditions on the communication digraph, the feedback gains, and the allowed upper bound of the delays to ensure containment control of the multi-agent systems under the different containment control algorithms are given. Finally, numerical simulations are presented to demonstrate theoretical results.

Control design for synchronisation of identical linear multi-agent systems

ABSTRACTIn this paper, we study the state synchronisation problem of multi-agent systems subject to external additive perturbations. We consider high-order linear time-invariant multi-agent systems whose communication topology is encoded by an undirected and connected graph. We propose an control design technique based on a decentralised output feedback controller. We give sufficient conditions to ensure state synchronisation with bounded gain using a Lyapunov-based approach. These conditions are characterised in terms of matrix inequalities. Since these matrix inequality conditions are non-convex and cannot be solved straightforwardly, we propose a relaxation technique and an effective numerical procedure to design a suitable controller with guaranteed performance on the multi-agent distributed closed loop.

Containment analysis and design for general linear multi-agent systems with time-varying delays

Containment analysis and design problems for general high-order linear time-invariant multi-agent systems with time-varying delays are studied, where the interaction topology is directed. Using the state information of each agent and neighboring agents, a protocol with time-varying delays is constructed, where the motion modes of the leaders can be specified. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with time-varying delays to achieve containment are proposed which only include four linear matrix inequalities independent of the number of agents. Moreover, an approach to determine the gain matrices in the protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

Formation-containment control for high-order linear time-invariant multi-agent systems with time delays

Formation-containment analysis and design problems for time-delayed high-order linear time-invariant multi-agent systems with directed interaction topologies are studied. Firstly, protocols with time delays are presented for leaders and followers, where the formation for leaders can be time-varying. Then formation-containment problems for time-delayed multi-agent systems are transformed into asymptotic stability problems of time-delayed systems. Sufficient conditions for multi-agent systems to achieve formation-containment are proposed, which include eight linear matrix inequalities independent of the number of leaders and followers. Furthermore, an explicit expression of the formation reference function for leaders is derived, where the motion modes of formation reference can be specified. An approach to determine the gain matrices in the protocols is given using the method of changing variables. Finally, numerical simulations are provided to demonstrate theoretical results.

Formation Control for High-Order Linear Time-Invariant Multiagent Systems With Time Delays

Formation control problems for high-order linear time-invariant multiagent systems with time delays are investigated. First, a general time-varying formation control protocol is proposed. Then, based on consensus approaches, necessary and sufficient conditions for multiagent systems to achieve a given time-varying formation are presented. An explicit expression of the time-varying formation reference function is also given. It is shown that the motion modes of the formation reference can be specified. Furthermore, necessary and sufficient conditions for formation feasibility are proposed. An approach to expand the feasible formation set and an algorithm to design the protocol for multiagent systems to achieve time-varying formations are provided, respectively. Finally, numerical simulations are presented to demonstrate theoretical results.