Computational approaches for mixed integer optimal control problems with indicator constraints
Optimal control problems with mixed integer control functions and logical implications, such as a state-dependent restriction on when a control can be chosen (so-called indicator or vanishing constraints) frequently arise in practice. A prominent example is the optimal cruise control of a truck. As...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
5 October 2018
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| In: |
Vietnam journal of mathematics
Year: 2018, Volume: 46, Issue: 4, Pages: 1023-1051 |
| ISSN: | 2305-2228 |
| DOI: | 10.1007/s10013-018-0313-z |
| Online Access: | Verlag, Volltext: https://doi.org/10.1007/s10013-018-0313-z
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| Author Notes: | Michael N. Jung, Christian Kirches, Sebastian Sager, Susanne Sass |
| Summary: | Optimal control problems with mixed integer control functions and logical implications, such as a state-dependent restriction on when a control can be chosen (so-called indicator or vanishing constraints) frequently arise in practice. A prominent example is the optimal cruise control of a truck. As every driver knows, admissible gear choices critically depend on the current velocity. A large variety of approaches has been proposed on how to numerically solve this challenging class of control problems. We present a computational study in which the most relevant of them are compared for a reference model problem, based on the same discretization of the differential equations. This comprehends dynamic programming, implicit formulations of the switching decisions, and a number of explicit reformulations, including mathematical programs with vanishing constraints in function spaces. We survey all of these approaches in a general manner, where several formulations have not been reported in the literature before. We apply them to a benchmark truck cruise control problem and discuss advantages and disadvantages with respect to optimality, feasibility, and stability of the algorithmic procedure, as well as computation time. |
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| Item Description: | Gesehen am 07.11.2019 |
| Physical Description: | Online Resource |
| ISSN: | 2305-2228 |
| DOI: | 10.1007/s10013-018-0313-z |