On the optimal control of hybrid systems: Optimization of trajectories, switching times, and location schedules

Abstract

A class of hybrid optimal control problems is formulated and a set of necessary conditions for hybrid system trajectory optimality is presented. These conditions constitute generalizations of the standard Maximum Principle (MP). Employing these conditions, we propose a class of general Hybrid Maximum Principle (HMP) based algorithms for hybrid systems optimization; these algorithms and the associated theory appear to be significantly simpler than some of the recently proposed algorithms (see [13], [14], for example). Using results from the theory of penalty function methods and Ekeland's variational principle we show the convergence of these algorithms under reasonable assumptions. The efficacy of the proposed algorithms is illustrated via several computational examples. © Springer-Verlag Berlin Heidelberg 2003.