Minimal Time Problem with Impulsive Controls

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• 作者：Karl Kunisch ; Zhiping Rao
• 关键词：Optimal control ; Impulsive differential equations ; Hamilton–Jacobi–Bellman equations
• 刊名：Applied Mathematics & Optimization
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：75
• 期：1
• 页码：75-97
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Phy
• 出版者：Springer US
• ISSN：1432-0606
• 卷排序：75

文摘

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton–Jacobi–Bellman equation in the viscosity sense. A numerical example for a rider-swing system is presented and it is shown that the reachable set is enlargered by allowing for impulsive controls, when compared to nonimpulsive controls.