Minimal Time Problem with Impulsive Controls

Karl Kunisch; Zhiping Rao

doi:10.1007/s00245-015-9324-2

Minimal Time Problem with Impulsive Controls

Karl Kunisch, Zhiping Rao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	75-97
Number of pages	23
Journal	Applied Mathematics and Optimization
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00245-015-9324-2
Publication status	Published - 1 Feb 2017
Externally published	Yes

Keywords

Hamilton–Jacobi–Bellman equations
Impulsive differential equations
Optimal control

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10.1007/s00245-015-9324-2

Cite this

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abstract = "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.",

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AB - 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.

KW - Hamilton–Jacobi–Bellman equations

KW - Impulsive differential equations

KW - Optimal control

UR - https://www.scopus.com/pages/publications/84947559650

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Minimal Time Problem with Impulsive Controls

Abstract

Keywords

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