Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

Submission Status:under review
  • We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the resulting subproblems as suitably chosen mixed-integer optimal control problems on subintervals in time. An iterative procedure then ensures continuity of the states at the boundaries of the subintervals via co-state information encoded in virtual controls. We prove convergence of this iterative scheme for discrete-continuous linear-quadratic problems and present numerical results both for linear-quadratic as well as nonlinear problems.

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Author:Falk Hante, Richard Krug, Martin Schmidt
Document Type:Preprint
Language:English
Date of Publication (online):2021/08/17
Date of first Publication:2021/08/17
Release Date:2021/08/17
Tag:Convergence; Mixed-integer nonlinear optimization; Mixed-integer optimal control problems; Time-domain decomposition
Page Number:32
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Humboldt-Universität zu Berlin
Universität Trier
Subprojects:A03
A05
B08
C08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International