Fixed time formation control for heterogeneous multi‐agent systems with partial unknown control directions

Abstract

SummaryThis article studies the fixed‐time time‐invariant formation control problem for a class of uncertain nonlinear heterogeneous multi‐agent systems (HMASs) with actuator faults and partial unknown control directions. Throughout the formation process, the possibility of actuator faults in systems and unknown control directions between individual agents are taken into account. Lipschitz conditions are introduced to identify the continuous uncertain nonlinear functions. To estimate the agents' local immeasurable states in HMASs, a distributed fixed‐time observer is proposed, which can ensure that the states of follower agents are observed in fixed time. In addition, a distributed formation fault‐tolerant control scheme will handle actuator faults. By designing a Nussbaum function, the problem of partial unknown control directions for HMASs can be solved in fixed time. Based on the fixed time stability theory, it is proved that the closed‐loop stability and the tracking performance can be guaranteed in fixed time, that is, the achieved time is independent of any initial states. In the end, a simulation example is given to testify the effectiveness of the proposed control method.