Lipschitz continuity of the value function in mixed-integer optimal control problems

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• 作者：Martin Gugat ; Falk M. Hante
• 关键词：Parametric optimal control ; Parametric switching control ; Parametric optimization ; Sensitivity ; Mixed ; integer optimal control problems ; Optimal value function ; Lipschitz continuity
• 刊名：Mathematics of Control, Signals, and Systems
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：29
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Control, Robotics, Mechatronics; Communications Engineering, Networks;
• 出版者：Springer London
• ISSN：1435-568X
• 卷排序：29

文摘

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.