Solution of the classical regulation problem by optimal controls of linear-quadratic problems

The basic problem of the classical regulation theory in the bounded control class is considered. Optimal control methods are used to construct the regulator work algorithm. These methods perform feedback implementation in the real-time mode. The feedback transfers the system from one equilibrium condition vicinity into another one with high transient quality. It stabilizes the system according to the new equilibrium condition. To solve the problem the feedback optimal control realization of linear-quadratic problem with restrictions is suggested. The results are illustrated with the example of the linear dynamical system regulation of the fourth order.