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 proceedingChapter

9 Scopus citations


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 languageEnglish (US)
Title of host publicationIFIP Advances in Information and Communication Technology
PublisherSpringer Nature
Number of pages10
ISBN (Print)9783642360619
StatePublished - 2013
Externally publishedYes

Bibliographical 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.


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