Non-equilibrium transient trajectory shaping control via multiple Barrier Lyapunov Functions for a class of nonlinear systems

This paper presents a non-equilibrium transient trajectory shaping (NETTS) control technique based on a set of Barrier Lyapunov Functions for single-input-single-output strict feedback nonlinear systems. The trajectory shapes of the system outputs or tracking errors during the course of convergence to the equilibrium points are important for some physical systems (e.g. some hybrid systems) where reference signals frequently jump. A smooth trajectory shaping control law consisting of a unidirectional switching mechanism and a control signal continuous approximation method is proposed to ascertain that the system tracking error transient trajectory travels within a shaped-boundary while approaching zero. A numerical example is utilized to show the performance of the proposed NETTS control.