Formation tracking control of fractional-order multi-agent systems with fixed-time convergence

Abstract

In this article, the fixed-time formation problem in fractional-order multi-agent systems is addressed. By using the Reimann–Liouville fractional derivative, the memory effects are considered in the dynamics of agents. The goal is to design distributed controllers for such agents of fractional order to achieve formation with a fixed-time convergence rate. To solve this problem, a fractional-order control protocol with a neighborhood-based error variable is proposed. By using the fixed-time Lyapunov stability theorem, it has been theoretically shown that the fixed-time formation tracking can be achieved within a certain settling time, and the upper bound of the settling time has been obtained explicitly. The proposed upper bound does not depend on the initial conditions. Finally, several simulations are worked out to verify the theoretical results. The superiority of the proposed method over finite-time protocols has been illustrated.