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

    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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