Subsystem Level Optimal Control and Filtering of Non-Classically Damped Matrix Second-Order Linear Mechanical Stochastic Systems

Abstract

Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, civil, aerospace engineering, and related fields. In this paper, we show how to optimally control matrix second-order systems using locally optimal Kalman filters corresponding to scalar second-order subsystems and how to find the corresponding filter and linear-quadratic (LQ) controller optimal gains at the subsystem level. The globally optimal linear-quadratic controller and the globally optimal Kalman filter and obtained in terms of locally optimal LQ controllers and locally optimal scalar second-order parallel Kalman filters. Conditions are established under which the presented procedure is applicable. Examples are included to demonstrate the efficiency of the proposed technique.