Distributed adaptive fixed-time formation tracking for heterogeneous multi-agent systems

Abstract

This article investigates the problem of fixed-time time-varying formation tracking control (FTC) for heterogeneous linear multiagent systems (MASs) under the directed communication graph. It is assumed that the Laplacian matrix associated with the communication graph is unavailable and that the system matrices of the leader are only available to its neighboring followers. This differs from many existing works on fixed-time FTC problems where the communication graphs are typically undirected and protocol designs often rely on certain global information. A novel distributed observer is first put forward to estimate both the state and system matrices of the leader in fixed time. Then, an adaptive scheme is developed to solve the time-varying regulator equations resulting from the estimated leader system matrices in fixed time. Based on the proposed observer and the adaptive solutions to the regulator equations, a distributed adaptive fixed-time FTC protocol is further proposed via coordinate transformation techniques. It is shown that our proposed controllers do not require the input matrices of the followers to be of full row rank. It is also shown that the concerned fixed-time FTC problem can be solved with the proposed fixed-time FTC strategy in a distributed manner. Our results can be directly applied to solve both the adaptive fixed-time cooperative output regulation problem and the leader-following consensus problems of MASs under the directed graph. Finally, the effectiveness of the proposed fixed-time FTC strategy is demonstrated through a numerical example.