Lipschitz continuity of the value function in mixed-integer optimal control problems
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We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show that the optimal value depends locally Lipschitz continuously on perturbations of the initial data and the costs under rather natural assumptions. We prove a similar result for perturbations of the initial data, the constraints and the costs for problems involving linear dynamics, convex costs and convex constraints under a Slater-type constraint qualification. We show by an example that these results are in a sense sharp.
KeywordsParametric optimal control Parametric switching control Parametric optimization Sensitivity Mixed-integer optimal control problems Optimal value function Lipschitz continuity
This work was supported by the DFG Grant CRC/Transregio 154, projects C03 and A03. The authors thank the reviewers and the associate editor for the constructive suggestions.
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