Least squares methods for H∞ control-oriented system identification

Abstract

This paper presents a series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies. These algorithm are applicable to a broad class of stable, distributed, linear, shift-invariant plants. The a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant, an upper bound on a certain gain associated with the unknown plant, and an upper bound on the noise level. The a posteriori data information consists of a finite number of noisy point frequency response estimates of the unknown plant. The specific contributions of this paper are to examine the extent to which certain standard Hilbert space or least squares methods are applicable to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> system identification problem considered. Results are established that connect the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> error of the least square methods to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> error needed for control-oriented system identification. In addition, the notion of a posteriori error bounds is introduced and used to establish sequentially optimal or adaptive algorithms based on these filbert space approaches.