Solving inverse optimal control problems via value functions to global optimality

Stephan Dempe (), Felix Harder (), Patrick Mehlitz () and Gerd Wachsmuth ()
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Stephan Dempe: Technische Universität Bergakademie Freiberg
Felix Harder: Brandenburgische Technische Universität Cottbus-Senftenberg
Patrick Mehlitz: Brandenburgische Technische Universität Cottbus-Senftenberg
Gerd Wachsmuth: Brandenburgische Technische Universität Cottbus-Senftenberg

Journal of Global Optimization, 2019, vol. 74, issue 2, No 5, 297-325

Abstract: Abstract In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard regularity conditions like Robinson’s CQ are violated at all the feasible points of this surrogate problem. It is, however, shown that locally optimal solutions of the problem solve a Clarke-stationarity-type system. Moreover, we relax the feasible set of the surrogate problem iteratively by approximating the lower level optimal value function from above by piecewise affine functions. This allows us to compute globally optimal solutions of the original inverse optimal control problem. The global convergence of the resulting algorithm is shown theoretically and illustrated by means of a numerical example.

Keywords: Bilevel optimal control; Global optimization; Inverse optimal control; Optimality conditions; Solution algorithm; 49K20; 49M20; 49N45; 90C26; 90C48 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-019-00758-1

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