Title

HAMILTON-JACOBI EQUATIONS AND TWO-PERSON ZERO-SUM DIFFERENTIAL GAMES WITH UNBOUNDED CONTROLS

Authors

Authors

H. Qiu;J. M. Yong

Comments

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Abbreviated Journal Title

ESAIM-Control OPtim. Calc. Var.

Keywords

Two-person zero-sum differential games; unbounded control; Hamilton-Jacobi equation; viscosity solution; H-INFINITY CONTROL; VISCOSITY SOLUTIONS; ISAACS EQUATIONS; UNIQUENESS; EXISTENCE; BELLMAN; REPRESENTATION; COST; Automation & Control Systems; Mathematics, Applied

Abstract

A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton-Jacobi-Isaacs equations, respectively. Consequently, when the Isaacs' condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of the controls, the corresponding upper and lower Hamiltonians grow super linearly in the gradient of the upper and lower value functions, respectively. A uniqueness theorem of viscosity solution to Hamilton-Jacobi equations involving such kind of Hamiltonian is proved, without relying on the convexity/concavity of the Hamiltonian. Also, it is shown that the assumed coercivity conditions guaranteeing the finiteness of the upper and lower value functions are sharp in some sense.

Journal Title

Esaim-Control Optimisation and Calculus of Variations

Volume

19

Issue/Number

2

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

404

Last Page

437

WOS Identifier

WOS:000317594900005

ISSN

1292-8119

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