8.3    Certainty-Equivalent Filters (CEFs)

We discuss in this section a class of estimators for the nonlinear system (8.1) which we refer to as “certainty-equivalent” worst-case estimators (see also [139]). The estimator is constructed on the assumption that the asymptotic value of x^ equals x, and the gain matrices are designed so that they are not functions of the state vector x, but of x^ and y only. We begin with the one degree-of-freedom (1-DOF) case, then we discuss the 2-DOF case. Accordingly, we propose the following class of estimators:

1acef:{ x^˙=f(x^)+g1(x^)w^+L^(x^,y)(yh2(x^)k21(x^)w)z^=h2(x^)z˜=yh2(x^)

(8.32)

where z^=y^m is the estimated output, z˜m is the new penalty variable, w^ is the estimated ...

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