System-Level Recurrent State Estimators for Affine Systems Subject to Data Losses Modeled by Automata

This paper proposes a robust output feedback state estimator for uncertain/bounded-error affine systems subject to data losses modeled by an automaton. Specifically, by introducing a novel property known as recurrent recovery, where the estimation errors are required to be recurrent to some minimum recovery levels at each node of the data loss automata, we design a robust estimator design that guarantees that the state estimation errors remain bounded in a recurrent manner despite worst-case realizations of process and sensor noise/uncertainties in addition to missing data. Our design can directly deal with infinite-horizon missing data specifications modeled by automata by recasting the problem into multiple finite-horizon problems of varying lengths, which results in an optimization-based approach with only a finite number of constraints. Moreover, our design is built upon system-level parameterization and for this purpose, we propose a novel affine output feedback strategy that also contributes to the literature of finite-horizon optimal control.