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

A first-order partial differential Hamilton-Jacobi equation and the gu aranteed-control problem which corresponds to it are examined. The gen eralized minimax solution of the Hamilton-Jacobi equation is the price function of the control problem. The problem of constructing the pric e function, the solution of which facilitates the finding of the optim al strategies, is investigated. Approximating (grid) schemas for the a pproximate computation of the minimax solution which use finite-differ ence operators based on the constructs of differential game theory and of convex and nonsmooth analysis are proposed. The convergence of the se schemas is substantiated. Illustrative examples are presented.