APPROXIMATION SCHEMAS AND FINITE-DIFFERENCE OPERATORS FOR CONSTRUCTING GENERALIZED SOLUTIONS OF HAMILTON-JACOBI EQUATIONS

A first-order partial differential Hamilton-Jacobi equation and the guaranteed-control problem which corresponds to it are examined. The generalized minimax solution of the Hamilton-Jacobi equation is the price function of the control problem. The problem of constructing the price function, the solution of which facilitates the finding of the optimal strategies, is investigated. Approximating (grid) schemas for the approximate computation of the minimax solution which use finite-difference operators based on the constructs of differential game theory and of convex and nonsmooth analysis are proposed. The convergence of these schemas is substantiated. Illustrative examples are presented.