Fixed-Time Formation Tracking Control of Nonlinear Multi-Agent Systems with Directed Topology and Disturbance

• Published in: Mathematics (Basel) Vol. 11; no. 13; p. 2849
• Main Authors: Luo, Zhiyong, Liu, Hongliang, Ouyang, Zigen
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2023
• Subjects: Adaptive control; Algebraic topology; Analysis; backstepping method; Communication; Control; Design; Euclidean space; formation control; Graph theory; Multi-agent systems; Multiagent systems; Nonlinear control; Nonlinear systems; Nonlinear theories; Topology; Tracking control; China
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11132849

In this paper, we study the fixed-time formation (FixF) control problem for the nonlinear second-order multi-agent systems (MASs) with directed graph, where all agents are subject to communication disturbances. To overcome the bounded disturbance of communication and to guarantee the realization of predesignated formation within a fixed-time, a suitable FixF control protocol based on the backstepping method is proposed. Furthermore, to eliminate the dependence of the control parameters on global information, a new adaptive FixF control protocol is provided to combine with some mild conditions of control gain such that the formation with acceptable bounded error of MASs can be achieved within a fixed-time. Finally, the theoretical results are verified by two simulation examples, one of the simulation examples is that we set the desired formation as a regular octagon and the desired formation motion trajectory as a circle, the results show that all agents can form formation motion within a fixed-time.