Arbitrary settling time control with prescribed performance for high-order nonlinear systems

This paper studies an arbitrary convergence time tracking controller design problem for high-order nonlinear systems. Our aim is to enhance the existing free-will arbitrary time control (FATC), which cannot track time-varying reference signals. To do so, a new nonautonomous equation is firstly introduced to enable an arbitrary settling time stability for one-order systems. Then, a prescribed performance control (PPC) technology is integrated for general high order systems. By a backstepping Lyapunov analysis with iteratively contructed nonautonomous equations, it is proved that the closed-loop system satisfies the prescribed performance and all signals of the closed-loop system are arbitrary settling time stable (ASTS). Compared with the existing results, the tracking control problem with arbitrary convergence time is addressed by a continuous control law, which shows a better transient performance also. Simulation results confirm the effectiveness of the proposed control method.