A Proximal Point Based Approach to Optimal Control of Affine Switched Systems

Authors:
Vadim Azhmyakov;Michael V. Basin;Jörg Raisch
Affiliations:
Departamento de Control Automatico, CINVESTAV, Mexico D.F., Mexico 07360;Department of Physical and Mathematical Sciences, University of Nuevo Leon, San Nicolas de los Garza, Mexico;Fachgebiet Regelungssysteme, Technische Universität Berlin, Berlin, Germany 10587 and Systems and Control Theory Group, MPI for Dynamics of Complex Technical Systems, Magdeburg, Germany 39106
Venue:
Discrete Event Dynamic Systems
Year:
2012

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Abstract

This paper focuses on the proximal point regularization technique for a class of optimal control processes governed by affine switched systems. We consider switched control systems described by nonlinear ordinary differential equations which are affine in the input. The affine structure of the dynamical models under consideration makes it possible to establish some continuity/approximability properties and to specify these models as convex control systems. We show that, for some classes of cost functionals, the associated optimal control problem (OCP) corresponds to a conventional convex optimization problem 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 the gradient-type method and classic proximal point techniques.