Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

8.5    Discrete-Time Certainty-Equivalent Filters (CEFs)

In this section, we present the discrete-time counterpart of the the results of Section 8.3.1 which we referred to as “certainty-equivalent” worst-case estimators. It is also similarly apparent that the filter gain derived in equation (8.72) may depend on the estimated state, and this will present a serious stumbling block in implementation. Therefore, in this section we derive results in which the gain matrices are not functions of the state x, but of $\widehat{x}$ and y only. The estimator is constructed on the assumption that the asymptotic value of $\widehat{x}$ equals x. We first construct the estimator for the 1-DOF case, and then we discuss the 2-DOF case.

We reconsider the nonlinear discrete-time affine ...