Approximation theory for linear-quadratic-Guassian optimal control of flexible structures

This paper presents approximation theory for the linear-quadratic-Gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite-dimensional compensators that approximate closely the optimal compensator, which is infinite-dimensional. Design of the optimal compensator separates into an optimal linear-quadratic control problem and a dual optimal state estimation problem; the solution to each problem lies in the solution to an infinite-dimensional Riccati operator equation. The approximation scheme in the paper approximates the infinite-dimensional LQG problem with a sequence of finite-dimensional LQG problems defined for a sequence of finite-dimensional, usually finite-element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem.The finite-dimensional equations for numerical approximation ...