Optimal Parallel Controllers and Filters for a Class of Second-Order Linear Dynamic Systems

Abstract

Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, electrical, civil, and aerospace engineering. This class of systems also comes from the distributed parameter dynamic systems (systems described by partial differential equations) when they are approximated by linear dynamic systems. In this paper, we show how to design, for this class of systems, the globally optimal linear-quadratic controller and the globally optimal Kalman filter in terms of locally optimal linear-quadratic controllers and locally optimal scalar second-order Kalman filters. This simplifies computational requirements and allows full parallelism in information processing and feedback loop implementation. Conditions are established under which the presented procedure is applicable. Examples are included to demonstrate the efficiency of the proposed technique.