Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

Abstract

This paper is concerned with the fixed‐time coordinated tracking problem for a class of nonlinear multi‐agent systems under detail‐balanced directed communication graphs. Different from conventional finite‐time coordinated tracking strategies, the fixed‐time approach developed in this paper guarantees that a settling time bound is prescribed without dependence on initial states of agents. First, for the case of a single leader, a distributed protocol based on fixed‐time stability techniques is proposed for each follower to accomplish the consensus tracking in a fixed time. Second, in the presence of multiple leaders, a new distributed protocol is proposed such that states of followers converge to the dynamic convex hull spanned by those of leaders in a fixed time. In addition, for a class of linear multi‐agent systems, sufficient conditions that guarantee the fixed‐time coordinated tracking are provided. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

High Performance of an Adaptive Sliding Mode Controller under Varying Loads for Lifting-Type Autonomous Grounded Robot

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