Computation of Value Functions in Nonlinear Differential Games with State Constraints
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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.
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.
SponsorsThis 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).
PublisherSpringer Science + Business Media