Consensus Control of Heterogeneous Multi-agent Systems with Time-delays

時滯異構多智能體系統的趨同控制

Student thesis: Doctoral Thesis

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Award date27 Jun 2022

Abstract

Cooperative control of multi-agent systems has been a hot topic in the past decades owing to its broad application in various areas such as mobile robots, unmanned aerial vehicles and distributed sensor networks. Among all its research topics, consensus is a fundamental one. The objective of consensus is to design a distributed control strategy for each agent with the information only from its neighbors so that all agents reach an agreement on some common variable of interest. In many practical systems, time-delay is a very common phenomenon that often causes poor performance even instability. Due to the communication and transmission constraints in practice, multi-agent systems often suffer from three types of time-delays, that is, communication delays, input delays and output delays. All these three types of time-delays may lead to the performance degradation or even instability of the concerned system, and should be taken into account when designing consensus protocols of multi-agent systems. As a result, the study on multi-agent systems with time-delays has been attracting considerable attention from the control community in the past years. However, recent literature review reveals that few works consider multi-agent systems within the presence of all three time-delays, that is, communication, input and output delays at the same time. This motivates investigations of this thesis.

This thesis investigates the consensus problem of heterogeneous multi-agent systems with those three types of time-delays. The main results of this thesis can be summarized as follows.

Firstly, the consensus problem of heterogeneous continuous-time multi-agent systems with communication, input and output time-delays is studied. An observer-predictor is designed to estimate the future states of each agent, and then a distributed dynamic controller based on this observer-predictor is proposed to solve the concerned problem. Switching and directed communication topologies are considered in this work. It is shown that the closed-loop control system can reach consensus for arbitrarily large yet bounded time-varying communication delays, time-varying input delays and constant output delays.

Secondly, the leader-following consensus problem of heterogeneous continuous-time multi-agent systems under switching and directed topologies is investigated. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established. An adaptive distributed observer, taking into consideration of communication time-delays, is proposed for each follower to estimate the leader's system matrices and state. Then a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multi-agent system achieves the leader-following output consensus.

Thirdly, the leader-following output consensus problem is addressed for heterogeneous discrete-time multi-agent systems with communication time-delays. Similar to the continuous-time counterpart, an adaptive distributed observer taking into consideration of communication time-delays is proposed for discrete-time case. By using the proposed distributed adaptive observer, a distributed controller is proposed for each agent. It is shown that under the proposed controller, the tracking errors between the outputs of all the agents and the output of the leader converge to zero asymptotically without any global graph information.

Finally, the leader-following output consensus problem for heterogeneous discrete-time multi-agent systems with more complicated time-delays including communication, input and output time-delays is studied. By using the predictor and adaptive distributed observer, a distributed predictor-based controller is designed. The proposed controller is independent of any global information. It is shown that the outputs of all the followers synchronize to the output of the leader asymptotically.