ASYMPTOTICS OF SOLUTION FOR SINGULARLY PERTURBED NONLINEAR DISCRETE PERIODIC OPTIMAL CONTROL PROBLEMS

摘要

The asymptotic expansion of the solution of a singularly perturbed nonlinear discrete time periodic optimal control problem is constructed as series with respect to non-negative integer powers of a small parameter. The terms of asymptotic expansion are the solutions of optimal control problems which are essentially simpler than the original perturbed problem. The solvability of the perturbed problem is established in the neighborhood of a solution of the simpler non-perturbed problem of the lower dimension. The estimates are obtained for the proximity of the approximate solutions to the exact one. The nice property is proved, namely, the values of the minimized functional do not increase when higher-order approximations to the optimal control are used. Numerical examples are given in order to illustrate the method proposed.