Prescribed Performance Filtering for Generation of Smooth Reference Trajectory

This paper is concerned with the problem of generating smooth reference trajectories by filtering, for backstepping control designs for nonlinear systems. To solve this problem, a prescribed performance filtering approach is proposed. Our filter is driven by an input signal which is generated recursively. In each design step, a barrier function is employed to confine the filtering error within the predefined bound. In this way, the filtered reference is not only smooth but also approximate the original reference with any high accuracy. The simulation results on the tracking control of a Van der Pol system illustrate the effectiveness and superiority of our approach.