Asymptotical Method for Solving the Singularly Perturbed Linear Problem of Terminal Control

摘要

The linear problem of terminal control for a singularly perturbed system is considered. 'Some functional constraints of the equality type are imposed on the right end of the trajectories and the values of multidimensional controls are bounded in the Euclidean norm. An algorithm is proposed that allows one to construct asymptotical approximations of arbitrary order to the solution to the problem considered. Its main advantage is that the initial problem of optimal control splits into two unperturbed problems of lower dimensions.