Computational approaches for mixed integer optimal control problems with indicator constraints

• Verfasst von: Jung, Michael [VerfasserIn]
• Verfasst von: Kirches, Christian [VerfasserIn]
• Verfasst von: Sager, Sebastian [VerfasserIn]
• Verfasst von: Sass, Susanne [VerfasserIn]
• Titel: Computational approaches for mixed integer optimal control problems with indicator constraints
• Verf.angabe: Michael N. Jung, Christian Kirches, Sebastian Sager, Susanne Sass
• E-Jahr: 2018
• Jahr: 5 October 2018
• Umfang: 29 S.
• Fussnoten: Gesehen am 07.11.2019
• Titel Quelle: Enthalten in: Vietnam journal of mathematics
• Ort Quelle: Singapore : Springer, 1999
• Jahr Quelle: 2018
• Band/Heft Quelle: 46(2018), 4, Seite 1023-1051
• ISSN Quelle: 2305-2228
• DOI: doi:10.1007/s10013-018-0313-z
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 49-04
• Sach-SW: 49M37
• Sach-SW: 65K05
• Sach-SW: 90-08
• Sach-SW: 90C30
• Sach-SW: 90C33
• Sach-SW: 90C39
• Sach-SW: 90C59
• Sach-SW: 90C90
• Sach-SW: 93B40
• Sach-SW: Cruise control
• Sach-SW: Dynamic programming
• Sach-SW: Heavy-duty truck
• Sach-SW: Indicator constraints
• Sach-SW: MINLP
• Sach-SW: Mixed integer optimal control
• Sach-SW: Partial outer convexification
• Sach-SW: Switched systems
• Sach-SW: Switching function
• Sach-SW: Vanishing constraints
• K10plus-PPN: 1041419902

Abstract

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.