Sub- and superoptimality principles and construction of almost optimal strategies for differential games in Hilbert spaces
نویسنده
چکیده
We prove suband superoptimality principles of dynamic programming and show how to use the theory of viscosity solutions to construct almost optimal strategies for two-player, zero-sum differential games driven by abstract evolution equations in Hilbert spaces.
منابع مشابه
Stochastic differential inclusions of semimonotone type in Hilbert spaces
In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...
متن کاملVerification theorem and construction of -optimal controls for control of abstract evolution equations
We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a sufficient condition for optimality. Moreover we prove suband superoptimality principles of dynamic programming and give an explicit construction of -optimal...
متن کاملSolving multi-order fractional differential equations by reproducing kernel Hilbert space method
In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...
متن کاملVeri cation theorem and construction of -optimal controls for control of abstract evolution equations
We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial di erential equations. We introduce and prove a veri cation theorem which provides a su cient condition for optimality. Moreover we prove suband superoptimality principles of dynamic programming and present an explicit construction of -optimal ...
متن کاملOptimal Feedback Control of Fractional Semilinear Integro-differential Equations in The Banach Spaces
Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...
متن کامل