Computation of Value Functions in Nonlinear Differential Games with State Constraints

Handle URI:
http://hdl.handle.net/10754/597821
Title:
Computation of Value Functions in Nonlinear Differential Games with State Constraints
Authors:
Botkin, Nikolai; Hoffmann, Karl-Heinz; Mayer, Natalie; Turova, Varvara
Abstract:
Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.
Citation:
Botkin N, Hoffmann K-H, Mayer N, Turova V (2013) Computation of Value Functions in Nonlinear Differential Games with State Constraints. System Modeling and Optimization: 235–244. Available: http://dx.doi.org/10.1007/978-3-642-36062-6_24.
Publisher:
Springer Science + Business Media
Journal:
IFIP Advances in Information and Communication Technology
KAUST Grant Number:
KSA-C0069; UK-C0020
Issue Date:
2013
DOI:
10.1007/978-3-642-36062-6_24
Type:
Book Chapter
ISSN:
1868-4238; 1861-2288
Sponsors:
This work was supported by the German Research Society (Deutsche Forschungsgemeinschaft) in the framework of the intention “Optimization with partial differential equations” (SPP 1253) and by Award No KSA-C0069/UK-C0020, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorBotkin, Nikolaien
dc.contributor.authorHoffmann, Karl-Heinzen
dc.contributor.authorMayer, Natalieen
dc.contributor.authorTurova, Varvaraen
dc.date.accessioned2016-02-25T12:57:18Zen
dc.date.available2016-02-25T12:57:18Zen
dc.date.issued2013en
dc.identifier.citationBotkin N, Hoffmann K-H, Mayer N, Turova V (2013) Computation of Value Functions in Nonlinear Differential Games with State Constraints. System Modeling and Optimization: 235–244. Available: http://dx.doi.org/10.1007/978-3-642-36062-6_24.en
dc.identifier.issn1868-4238en
dc.identifier.issn1861-2288en
dc.identifier.doi10.1007/978-3-642-36062-6_24en
dc.identifier.urihttp://hdl.handle.net/10754/597821en
dc.description.abstractFinite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.en
dc.description.sponsorshipThis work was supported by the German Research Society (Deutsche Forschungsgemeinschaft) in the framework of the intention “Optimization with partial differential equations” (SPP 1253) and by Award No KSA-C0069/UK-C0020, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Science + Business Mediaen
dc.subjectDifferential gamesen
dc.subjectfinite-difference schemesen
dc.subjectnon-terminal payoff functionalsen
dc.subjectstate constraintsen
dc.subjectvalue functionsen
dc.subjectviscosity solutionsen
dc.titleComputation of Value Functions in Nonlinear Differential Games with State Constraintsen
dc.typeBook Chapteren
dc.identifier.journalIFIP Advances in Information and Communication Technologyen
dc.contributor.institutionTechnische Universitat Munchen, Munich, Germanyen
kaust.grant.numberKSA-C0069en
kaust.grant.numberUK-C0020en
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