Optimal tracking controller design for non-linear non minimum-phase systems

An optimal tracking controller design approach for non-linear non minimum-phase systems based on the concept of modified optimal control is presented. We extend the existing design strategy of modified optimal control to non-linear time-variant systems, since tracking a desired trajectory results in a time-variant non-linear system for the tracking error. We obtain an optimal control law which achieves global asymptotic stability in the sense of Lyapunov and appropriate dynamics of the time-variant closed loop system. In addition, we present a new practically applicable procedure for finding time-variant Control Lyapunov Function candidates, which are necessary for all Lyapunov based controller synthesis methods. To demonstrate the efficiency and the advantages of the presented method a tracking controller is designed for the non minimum-phase model of the van de Vusse reaction.