Numerically Stable Approximations of Optimal Control Processes Associated with a Class of Switched Systems

In this contribution, we propose a numerical approach to optimal control processes governed by some specific switched systems. Our principal computational scheme can be characterized as an extension of the conventional proximal point method to optimal control problems (OCPs) with switched dynamical models. We study proximal based constructive approximations of the initial OCPs and establish the numerical stability (numerical consistency) of the resulting algorithm. We also discuss the practical implementability of the elaborated method and point some possible generalizations of our idea in the context of hybrid control systems.