Robust Stochastic Performance Optimization

Abstract

The problem of finding the controller that optimizes the expected H2-norm of an uncertain system is solved in closed form for a class of problems including such signal processing applications as feedforward design, channel equalization, noise cancellation etc. The method uses covariance information on model uncertainty and does therefore match information obtainable from standard system identification. The optimal controller is found by using a spectral factorization to rewrite the problem as an H2-problem for an extended system. The article puts a restrictions on where uncertain parameters enter. The need for hard bounds on parameters can then be avoided. The method also avoids the conservativeness related to designing for worst cases.