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Title: Minimal Time Problem with Impulsive Controls

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.

Authors:
 [1];  [2]
  1. University of Graz, Institute for Mathematics and Scientific Computing (Austria)
  2. Austrian Academy of Sciences, Radon Institute of Computational and Applied Mathematics (Austria)
Publication Date:
OSTI Identifier:
22617101
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 75; Journal Issue: 1; Other Information: Copyright (c) 2017 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; HAMILTON-JACOBI EQUATIONS; OPTIMAL CONTROL; PROGRAMMING; VISCOSITY

Citation Formats

Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at, and Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at. Minimal Time Problem with Impulsive Controls. United States: N. p., 2017. Web. doi:10.1007/S00245-015-9324-2.
Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at, & Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at. Minimal Time Problem with Impulsive Controls. United States. doi:10.1007/S00245-015-9324-2.
Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at, and Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at. Wed . "Minimal Time Problem with Impulsive Controls". United States. doi:10.1007/S00245-015-9324-2.
@article{osti_22617101,
title = {Minimal Time Problem with Impulsive Controls},
author = {Kunisch, Karl, E-mail: karl.kunisch@uni-graz.at and Rao, Zhiping, E-mail: zhiping.rao@ricam.oeaw.ac.at},
abstractNote = {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.},
doi = {10.1007/S00245-015-9324-2},
journal = {Applied Mathematics and Optimization},
number = 1,
volume = 75,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2017},
month = {Wed Feb 15 00:00:00 EST 2017}
}