Finite-time formation tracking for heterogeneous Euler–Lagrange systems with an uncertain leader

This paper discusses the finite-time time-varying formation tracking control problem of heterogeneous Euler–Lagrange systems with an uncertain leader. Unlike most existing works, where knowledge of the system dynamics of the leader node is required for follower agents in advance, this paper presents a distributed observer-based finite-time formation tracking control framework that operates independently of the system dynamic knowledge of the leader node. Firstly, two novel classes of finite-time adaptive distributed observers are constructed to estimate both the state and unknown dynamics of the leader system. The associated adaptation parameters can converge to the true values in finite time under an initial excitation condition, rather than the existing restrictive persistently exciting or cooperative finite-time excitation condition. Then, a finite-time formation tracking controller is developed based on the presented finite-time observers; with the help of Lyapunov stability theory, the finite-time formation tracking criterion for the considered system with an uncertain leader is derived from the constructed controller. Finally, a simulation example is provided to demonstrate the effectiveness of the presented finite-time formation tracking controller.