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

6 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 languageEnglish (US)
Title of host publicationIFIP Advances in Information and Communication Technology
PublisherSpringer Nature
Pages235-244
Number of pages10
ISBN (Print)9783642360619
DOIs
StatePublished - 2013
Externally publishedYes

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