Output transient trajectory shaping control for a class of nonlinear systems

This paper presents a transient trajectory shaping (TTS) control method for the SISO strict feedback nonlinear systems. The TTS control refers to explicitly constraining the system output tracking error transient trajectories within predesigned time-varying boundaries while they are converging to equilibrium. By this method, the boundaries of system output transient trajectories can be designed a priori according to the system transient control performance requirements in both symmetric and asymmetric ways. With a class of time-varying boundary functions, control laws can be devised by utilizing the enhanced differential unbounded function techniques. Such control laws can ascertain that the system output tracking errors travel within their respectively predesigned time-varying boundaries while converging to origin. To handle the control input exaggeration issue in TTS, input constraint control techniques are proposed to effectively reduce the required control input magnitude for second-order systems. A numerical example is utilized to show the effectiveness of the proposed TTS control methods.