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Computational approaches for mixed integer optimal control problems with indicator constraints. (English) Zbl 1405.49002
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.

49-04 Software, source code, etc. for problems pertaining to calculus of variations and optimal control
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C39 Dynamic programming
90C59 Approximation methods and heuristics in mathematical programming
90C90 Applications of mathematical programming
93B40 Computational methods in systems theory (MSC2010)
49L20 Dynamic programming in optimal control and differential games
Full Text: DOI
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