Polynomial solution of the continuous-time GMV control problem

Abstract

This paper deals with the solution of the generalized minimum variance (GMV) output tracking control problem for continuous-time SISO plants. The problem is approached by means of the polynomial method and the solution is achieved in the general case by solving three diophantine equations. Furthermore, since the existence of the solution cannot be ensured from the outset and the problem solvability does not ensure the properness of the solution, sufficient conditions are given to guarantee the problem solvability and the properness of the optimal controller. Finally, two simple examples clarify the theory and show the effectiveness of the GMV strategy in the case of very highly coloured measurement noise acting on the plant, with control and noise bandwidths overlapped