Computation of Value Functions in Nonlinear Differential Games with State Constraints

Nikolai Botkin; Karl-Heinz Hoffmann; Natalie Mayer; Varvara Turova

doi:10.1007/978-3-642-36062-6_24

Computation of Value Functions in Nonlinear Differential Games with State Constraints

Nikolai Botkin, Karl-Heinz Hoffmann, Natalie Mayer, Varvara Turova

Research output: Chapter in Book/Report/Conference proceeding › Chapter

7 Scopus citations

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.

Original language	English (US)
Title of host publication	IFIP Advances in Information and Communication Technology
Publisher	Springer Nature
Pages	235-244
Number of pages	10
ISBN (Print)	9783642360619
DOIs	https://doi.org/10.1007/978-3-642-36062-6_24
State	Published - 2013
Externally published	Yes

Access to Document

10.1007/978-3-642-36062-6_24

Cite this

@inbook{c0c0694d110c4b8eaced8f5da2fa61eb,

title = "Computation of Value Functions in Nonlinear Differential Games with State Constraints",

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. {\textcopyright} 2013 IFIP International Federation for Information Processing.",

author = "Nikolai Botkin and Karl-Heinz Hoffmann and Natalie Mayer and Varvara Turova",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KSA-C0069, UK-C0020 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2013",

doi = "10.1007/978-3-642-36062-6_24",

language = "English (US)",

isbn = "9783642360619",

pages = "235--244",

booktitle = "IFIP Advances in Information and Communication Technology",

publisher = "Springer Nature",

}

TY - CHAP

T1 - Computation of Value Functions in Nonlinear Differential Games with State Constraints

AU - Botkin, Nikolai

AU - Hoffmann, Karl-Heinz

AU - Mayer, Natalie

AU - Turova, Varvara

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KSA-C0069, UK-C0020 Acknowledgements: 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). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/597821

UR - http://link.springer.com/10.1007/978-3-642-36062-6_24

UR - http://www.scopus.com/inward/record.url?scp=84874495107&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36062-6_24

DO - 10.1007/978-3-642-36062-6_24

M3 - Chapter

SN - 9783642360619

SP - 235

EP - 244

BT - IFIP Advances in Information and Communication Technology

PB - Springer Nature

ER -

Computation of Value Functions in Nonlinear Differential Games with State Constraints

Abstract

Access to Document

Other files and links

Fingerprint

Cite this