Accession Number : ADA137939

Title :   Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman's and Isaacs' Equations.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Lions,P L ; Souganidis,P E

PDF Url : ADA137939

Report Date : Jan 1984

Pagination or Media Count : 37

Abstract : Recent work by the authors and others has demonstrated the connections between the dynamic programming approach to optimal control theory and to two-person, zero-sum differential games problems and the new notion of viscosity solutions of Hamilton-Jacobi PDE's introduced by M. G. Crandall and P. L. Lions. In particular, it has been proved that the dynamic programming principle implies that the value function is the viscosity solution of the associated Hamilton-Jacobi-Bellman and Isaacs equations. In the present work, it is shown that viscosity super- and subsolutions of these equations must satisfy some inequalities called super- and subdynamic programming principle respectively. This is then used to prove the equivalence between the notion of viscosity solutions and the conditions, introduced by A. Subbotin, concerning the sign of certain generalized directional derivatives. (Author)

Descriptors :   *Dynamic programming, *Partial differential equations, *Viscosity, *Solutions(General), Derivatives(Mathematics), Game theory, Control theory, Optimization, Functions(Mathematics), Continuity

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE