A Boundary Layer Method for Optimal Control of Singularly Perturbed Systems

摘要

A method is developed for approximating the solution of an optimally controlled singularly perturbed system. The method is applicable to both fixed and free end-point problems where in the latter problem a terminal cost is added to the performance index. Although the optimal solution is generally difficult to obtain using existing numerical algorithms, this method avoids such difficulties. The approximate solution is obtained by properly combining the solutions of three systems: a reduced 2n(1)-dimensional system, a left layer time invariant initial value n(2)-dimensional system, and a right layer time invariant initial value n(2)-dimensional system. The layer solutions can be interpreted as the results of two boundary layer regulators: one acting in forward time from the initial point and the other acting in reverse time from the end point. Example problems are worked which illustrate the method developed. (Author)