Optimal Feedback Control through Numerical Synthesis of Stabilization System

This paper presents a new two-step numerical approach to a solution of the optimal control problem with phase constraints named a synthesized optimal control. The stated problem combines two well-known tasks: the optimal control and the control system synthesis. Initially, the synthesis problem is considered and a feedback control is received that provides a steady state for the control object relative to some point in a state space. Then a sequence of points is searched in the state space, so that each of the points is stable in the state space of the object, so the object moves from the initial condition to terminal one by switching from one stabilization point to another in some time interval. It is shown in the paper that such approach allows to receive a solution that does not differ much from those of the optimal control problem considering the value of the quality criterion, but it works more stable in the presence of disturbances. At the same time such approach is much more applicable in real engineering tasks since some distinctions between the mathematical model of the control object and the real control object are smoothed over due to the first stabilization procedure of the approach. The paper includes a mathematical problem statement, the description of modern computational methods for its solution and computational example.