Set-Valued State Estimation for Nonlinear Uncertain Systems

Abstract

In previous chapters, we have concentrated on the problem of robust state estimation for the case in which the nominal model is linear. However, there are many applications of Kalman Filtering in which the underlying signal model is nonlinear. The approach which we will follow in this chapter is the set-valued state estimation approach such as presented in Chapter 4. We will model the uncertainty and disturbances in the system deterministically via a nonlinear integral constraint. This nonlinear integral constraint is an extension of the Integral Quadratic Constraint (IQC) considered in Chapter 4; see also [123]. However unlike Chapter 4, we will deal with the case in which the state equations defining the uncertain system are nonlinear. The results presented in this chapter are based on those in the papers [58,59]. It should be noted that the paper [11] also considers a related nonlinear setvalued state estimation problem. However in [11], the disturbance model is a disturbance model of the type given in [16] rather than a nonlinear integral constraint uncertainty model which allows for uncertain dynamics.