Approximate Synthesis of Optimal Control for Perturbed Systems with Invariant Norm

Abstract

We develop an effective method of constructing Bellman’s function and the optimal control for some classes of perturbed systems on a restricted time interval. The approach is based on the perturbation technique for solving the initial-value problem for the of Hamilton-Jacobi-Bellman equation. The efficiency of the method is essentially determined by the possibility of a complete solution of the corresponding unperturbed optimal control problem by using Schwartz’s functional inequality.