THE INVERSE PROBLEM OF OPTIMAL REGULATORS AND ITS APPLICATION

This paper presents a new solution to the inverse problem of linear optimal regulators to minimize a cost function and meet the requirements of relative stability in the presence of a constant but unknown disturbance. A state feedback matrix is developed using Lyapunov's second method. Moreover, the relationships between the state feedback matrix and the cost function are obtained, and a formula to solve the weighting matrices is suggested. The developed method is applied successfully to design the horizontal loops in the inertial navigation system.