FILTERING AND SMOOTHING IN AN H" SETTING

In this paper we consider the problems of filtering and smoothing for linear systems in an H" setting, i.e., the plant and measurement noises have bounded energies (are in L2), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered : in one case the initial condition is assumed known while in the other case the initial condition is not known but the initial condition, the plant and measurement noise are in some weighted ball of R"xL2. Both finite horizon and infinite horizon cases are considered. We present necessary and sufficient conditions for existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, develop algorithms that result in performance within the bounds. In case of smoothers we also present the optimal smoother.The approach uses basic quadratic optimization theory in time domain setting, as a consequence of which both linear time varying and time invariant systems can be considered with equal ease. (For linear time varying systems we consider only the finite horizon problems). Due to space limitations, most of the proofs are omitted here.

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