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Numerical solution of optimal control problems with explicit and implicit switches

Hans Georg Bock (bock***at***iwr.uni-heidelberg.de)
Christian Kirches (c.kirches***at***tu-bs.de)
Andreas Meyer (andreas.meyer***at***iwr.uni-heidelberg.de)
Andreas Potschka (andreas.potschka***at***iwr.uni-heidelberg.de)

Abstract: In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized disjunctive programming, we transform the problem into a counterpart one wherein discontinuities no longer appear implicitly. Instead, the new problem contains discrete decision variables and vanishing constraints. Recent results from the field of mixed-integer optimal control theory enable us to omit integrality constraints on variables, and allow to solve a relaxed optimal control problem. We use a ``first discretize, then optimize'' approach to solve the problem numerically. A direct method based on adaptive collocation is used for the discretization. The resulting finite dimensional optimization problems are mathematical programs with vanishing constraints, and we discuss numerical techniques to solve sequences of this challenging problem class. To demonstrate the efficacy and merit of our proposed approach, we investigate three benchmark problems for hybrid dynamic systems.

Keywords: switched systems; generalized disjunctive programming; optimal control; mixed-integer optimal control; direct transcription methods; mathematical programs with vanishing constraints

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Heidelberg University, INF 205, 69120 Heidelberg, 09/2017

Download: [PDF]

Entry Submitted: 11/15/2016
Entry Accepted: 11/15/2016
Entry Last Modified: 09/29/2017

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