DESIGN OF REDUCED-ORDER, H-2 OPTIMAL CONTROLLERS USING A HOMOTOPY ALGORITHM

The minimal dimension of a linear-quadratic-gaussian (LQG) compensator is almost always equal to the dimension of the design plant. This deficiency can lead to implementation problems when considering control design for high-order systems such as flexible structures and has led to the development of methodologies for the design of optimal (or near optimal) controllers whose dimension is less than that of the design plant. This paper presents a new (gradient-based) homotopy algorithm for the design of reduced-order, H-2 optimal controllers. An important result is the development of an efficient methodology for computation of the cost functional hessian which is required by the algorithm. The optimal controller is represented by a parameter vector and various parametrizations of the optimal controller are considered to reduce the algorithm dimensionality. The algorithm has been implemented in MAT-LAB and the results are illustrated using a benchmark, non-collocated flexible structural control problem. It is seen that the choice of a particular controller parametrization often introduces numerical ill-conditioning in the algorithm implementation.