Fixed-time Formation Tracking for Heterogeneous Linear Multi-agent Systems with A Nonautonomous Leader

This article studies the fixed-time time-varying formation (TVF) tracking control problem for heterogeneous multi-agent systems (HMASs) with a nonautonomous leader under a directed communication network. The primary objective is to design a TVF tracking protocol enabling the followers to form the desired TVF while simultaneously tracking the output of the nonautonomous leader in a fixed time. Firstly, a distributed fixed-time observer is proposed to estimate the state of the nonautonomous leader under a directed communication network. Then, utilizing coordinate transformation and sliding mode techniques, a fixed-time observer-based TVF tracking protocol is developed without requiring the full row rank assumption on the input matrix of the follower. It is proved via the Lyapunov stability theory that the fixed-time TVF tracking problem with a nonautonomous leader can be solved under the proposed protocol. Finally, the effectiveness of the proposed fixed-time TVF tracking control protocol is demonstrated by numerical examples.