An application of the proximal point algorithm to optimal control of affine switched systems

Abstract

This paper focuses on the proximal point regularization technique for a class of optimal control processes governed by affine switched systems. We consider some controllable dynamical systems described by nonlinear ordinary differential equations which are affine in the input. The affine structure of the control systems under consideration makes it possible to establish some continuity/approximability properties of the dynamical models and to characterize these dynamical models as convex control systems. We show that, for some classes of cost functionals, the associated optimal control problems (OCPs) correspond to the standard convex optimization problems in a suitable Hilbert space. The latter can be reliably solved using standard first-order optimization algorithms and consistent regularization schemes. In particular, we propose a conceptual numerical approach based on gradient-type methods and proximal point techniques.