Minimum variance control strategy for closed loop linear time invariant system

Abstract

To design one feedback controller in a closed loop linear time invariant system, the idea of minimum variance control is used to realise this goal. Two explicit forms corresponding to the closed loop system are considered, i.e., its general form and rational transfer function form respectively. Firstly one closed form solution of the minimum variance controller is derived in the general form of the closed loop linear time invariant system, and an optimisation algorithm is proposed to obtain controller in practice. Secondly in the rational transfer function form of the closed loop linear time invariant system, the minimum variance controller is determined, while guaranteeing the modified variances of output and input as small as possible.