SYNTHESIS OF OPTIMAL GUARANTEED CONTROL IN FINITE-DIFFERENCE APPROXIMATION SCHEMES

Procedures are proposed for synthesizing of optimal controls using the method of extremal aiming in the direction of the gradients of approx imations of the value functions in problems with terminal and integral discount functionals. The value functions are approximated by finite- difference operators for a Hamilton-Jacobi equation, using constructio ns of sub-and superdifferentials of local convex and concave closures. The dependence of the approximation stepsize on the phase space and t he time interval is investigated. It is shown that the trajectories ge nerated by a control synthesized by the proposed procedures are indeed optimal. The possibilities of the computational methods are illustrat ed by an example: the solution of a bimatrix evolutionary game with no n-linear dynamics generalizing the classical replicator models. (C) 19 97 Elsevier Science Ltd. All rights reserved.