Application of the small parameter method to the singularly perturbed linear-quadratic optimal control problem

This paper considers a control problem for a linear singularly perturbed system with minimum energy. The terminal state of the system and the transition time are given. We construct asymptotic approximations of optimal programmed control and optimal feedback control in the problem. A main advantage of the proposed algorithms is decomposing the initial optimal control problem into two unperturbed problems of smaller dimension.