Set-Valued State Estimation with Structured Uncertainty

Abstract

In this chapter, we will present a new formulation of the robust set-valued state estimation problem which enables us to present set-valued state estimation results for a class of uncertain systems with structured uncertainties. This class of uncertain systems is one in which the uncertainty is described by an “Averaged Integral Quadratic Constraint”(AIQC). This uncertainty description extends the standard integral quadratic constraint uncertainty description given in Chapter 4. The standard integral quadratic constraint defines a class of uncertainties which is extremely rich and allows for nonlinear time-varying dynamic uncertainties.Our new uncertainty description also allows for such a rich uncertainty class. Furthermore, it enables a tractable solution to be obtained for the set-valued state estimation problem in the case of structured uncertainty. Such problems have been found to be intractable using other representations of structured uncertainty.