In more detail, we present constructive and simple MHE design procedures which are tailored to the considered class of dynamical systems in order to guarantee important properties of the resulting estimation error dynamics. Furthermore, we develop computationally efficient MHE algorithms in which a suboptimal state estimate is computed at each time instant after an arbitrary and limited number of optimization algorithm iterations. In particular, we introduce a novel class of anytime MHE algorithms which ensure desirable stability and performance properties of the estimator for any number of optimization algorithm iterations, including the case of a single iteration per time instant.
In addition to the obtained theoretical results, we discuss the tuning of the performance criteria in proximity MHE given prior knowledge on the system disturbances and illustrate the theoretical properties and practical benefits of the proposed approaches with various numerical examples from the literature.
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