Approximately Optimal Stabilization of a Gyroscopic System with Many Degrees of Freedom and Slowly Varying Parameters

Abstract: The problem of stabilization of small oscillations of a gyroscopic system with many degrees of freedom and slowly varying parameters is considered and solved using Bellman’s principle of dynamic programming. The approximate procedures for the controller synthesis are based on the asymptotic solution of the Hamilton-Jacobi-Bellman equation by the averaging method. A quadratic optimality criterion is used, depending on the oscillation amplitudes of the system and control. The proposed method is applied to linear disturbances of the general type and those associated with a slow change in system parameters. The new approach allows the design of controllers in analytical form. © 2023, Pleiades Publishing, Ltd.