H2 optimal reduced order control design using a fuzzy logic methodology with bounds on system variances

There are practical reasons for controlling systems in such a way that variances of selected inputs and outputs are kept within specified limits. One way of designing control laws that achieve these objectives is by using a linear quadratic Gaussian (LQG) (or optimal H₂) control design method with an appropriate choice of the input and output weighting matrices. Since the LQG controller is of the same order as the plant being controlled, its practical implementation tends to be very difficult for higher order plants unless the controller order is reduced. This letter considers the design of H₂ optimal reduced order controllers to meet a set of variance constraints. This problem also involves the proper choice of the weighting matrices in the cost function. The fuzzy algorithm previously developed for the full-order variance constrained problem is shown to be applicable to the reduced order variance constrained problem. Three reduced order design schemes are developed and compared. Two schemes involve direct reduced order design and one scheme involves reduced order design using modified balanced truncation. The three schemes are compared using numerical experiments. The results clearly demonstrate the feasibility of reduced order H₂ optimal design that satisfy variance constraints on the system.