Optimal output trajectory design and tracking in preview-based nonperiodic tracking-transition switching for nonminimum-phase linear systems

In this article, the problem of nonperiodic tracking-transition switching with preview is considered, where, multiple switching between tracking and transition occur, and the output needs to track desired trajectory during the tracking sections, then rapidly transits to another point during the transition sections with no post-transition oscillations. Due to the coupling between the control of the tracking sections and that of the transition ones, these control objectives become challenging, particularly for nonminimum-phase systems. In the proposed approach, (1) the optimal desired output trajectory for the transition sections is designed through direct minimization of the output energy, and (2) the needed control input that maintains the smoothness of the system state across all tracking-transition switching instants is obtained by using a preview-based stable-inversion approach, and the needed preview time is quantified.