Optimal Synthesis and Predictive Stabilization of a Linear System

摘要

The problem of minimizing the mean square deviations of the trajectory of a linear nonstationary system from the equilibrium state on a given interval of time is studied by using scalar-valued control bounded with respect to the amplitude. The optimal synthesized control is constructed in an analytical form. Two procedures for stabilization are proposed; at each instant of time, these procedures take into account the future behavior of the system. The stability of the equilibrium state of the closed-loop system and the robustness of the synthesized control are studied.