Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288496 
Year of Publication: 
2020
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 78 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 575-623
Publisher: 
Springer US, New York, NY
Abstract: 
The combinatorial integral approximation (CIA) decomposition suggests solving mixed-integer optimal control problems by solving one continuous nonlinear control problem and one mixed-integer linear program (MILP). Unrealistic frequent switching can be avoided by adding a constraint on the total variation to the MILP. Within this work, we present a fast heuristic way to solve this CIA problem and investigate in which situations optimality of the constructed feasible solution is guaranteed. In the second part of this article, we show tight bounds on the integrality gap between a relaxed continuous control trajectory and an integer feasible one in the case of two controls. Finally, we present numerical experiments to highlight the proposed algorithm’s advantages in terms of run time and solution quality.
Subjects: 
Mixed-integer linear programming
Optimal control
Discrete approximations
Switched dynamic systems
Approximation methods and heuristics
JEL: 
M20
M27
B35
C11
C59
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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