Non-equilibrium transient trajectory shaping control via a three-stage switching method for a class of nonlinear systems

This paper presents a three-stage switching control method to deal with the non-equilibrium transient trajectory shaping (NETTS) control problem for a class of nonlinear systems. Through this method, the system tracking error non-equilibrium transient trajectory can be effectively shaped by constant boundaries and two pre-designed, exponentially-converging bounds. The tracking error is handled by a Barrier Lyapunov Function (BLF) in the first stage. Once the derivative of the tracking error reaches a desired negative value, the control law is switched into stage 2 where a trajectory shaping method is utilized by changing the coordinates and the trajectory of tracking error is bounded by two pre-designed, exponentially-converging boundaries. After the tracking error converging into a sufficiently small region around zero, the control law is switched to the BLF based method again for constraining the transient trajectory in the third stage. A numerical example is utilized to demonstrate the performance of the proposed three-stage NETTS switching control algorithm.