LQ preview state feedback with output regulation constraint

Recent developments in the theory of operator regulator equations enable us to approach various types of servo compensator design, which fall into distributed parameter systems. By regarding the preview system as a class of distrubuted parameter systems, this paper proposes a simple design method of LQ optimal preview control achieving output regulation. The key idea is to introduce a transformation of the fictitious delay, and to characterize the output regulation condition in terms of a matrix regulator equation. It is also explained that this finite-dimensional solvability condition is consistent with the infinite-dimensional output regulation theory.