On mixed-integer optimal control with constrained total variation of the integer control

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 vari...

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Vydáno v:Computational optimization and applications Ročník 78; číslo 2; s. 575 - 623
Hlavní autoři: Sager, Sebastian, Zeile, Clemens
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer US 01.03.2021
Springer Nature B.V
Témata:
Algorithms
Approximation methods and heuristics
Combinatorial analysis
Constraints
Convex and Discrete Geometry
Discrete approximations
Linear programming
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Mixed-integer linear programming
Nonlinear control
Operations Research
Operations Research/Decision Theory
Optimal control
Optimization
Statistics
Switched dynamic systems
Trajectory control
49M20
Discrete approximations
Optimal control
Approximation methods and heuristics
90C11
90B35
Switched dynamic systems
49M27
90C59
Mixed-integer linear programming
ISSN:1573-2894, 0926-6003, 1573-2894
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Shrnutí: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.
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ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-020-00244-5