Design Criteria for Uncertain Models with Structured and Unstructured Uncertainties?

This paper introduces and solves a weighted game-type cost criterion for estimation and control purposes that allows for a general class of uncertainties in the model or data. Both structured and unstructured uncertainties are allowed, including some special cases that have been used in the literature. The optimal solution is shown to satisfy an orthogonality condition similar to least-squares designs, except that the weighting matrices need to be modified in a certain optimal manner. One particular application in the context of state regulation for uncertain state-space models is considered. It is shown that in this case, the solution leads to a control law with design equations that are similar in nature to LQR designs. The gain matrix, however, as well as the Riccati variable, turn out to be statedependent in a certain way. Further applications of these game-type formulations to image processing, estimation, and communications are discussed in [1–3].