Robust optimal feedback for terminal linear-quadratic control problems under disturbances

We consider a linear dynamic system in the presence of an unknown but bounded perturbation and study how to control the system in order to get into a prescribed neighborhood of a zero at a given final moment. The quality of a control is estimated by the quadratic functional. We define optimal guaranteed program controls as controls that are allowed to be corrected at one intermediate time moment. We show that an infinite dimensional problem of constructing such controls is equivalent to a special bilevel problem of mathematical programming which can be solved explicitely. An easy implementable algorithm for solving the bilevel optimization problem is derived. Based on this algorithm we propose an algorithm of constructing a guaranteed feedback control with one correction moment. We describe the rules of computing feedback which can be implemented in real time mode. The results of illustrative tests are given.