Title

Hamilton-Jacobi Equations And Two-Person Zero-Sum Differential Games With Unbounded Controls

Keywords

Hamilton-Jacobi equation; Two-person zero-sum differential games; Unbounded control; Viscosity solution

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. © 2012 EDP Sciences, SMAI.

Publication Date

4-1-2013

Publication Title

ESAIM - Control, Optimisation and Calculus of Variations

Volume

19

Issue

2

Number of Pages

404-437

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1051/cocv/2012015

Socpus ID

84876565628 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84876565628

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