Finite horizon constrained control and bounded-error estimation in the presence of missing data

In this paper, we propose an optimization-based design technique for constrained control and bounded-error state estimation for affine systems in the presence of intermittent measurements. We treat the affine system as a switched system where the measurement equation switches between two modes based on whether a measurement exists or is missing, and model potential missing data patterns with a finite-length language that constrains the feasible mode sequences. Then, we introduce a novel property, equalized recovery, that generalizes the equalized performance property and that allows us to tolerate missing observations. By utilizing Q-parametrization, we show that a finite horizon optimal estimator/controller can be constructed using time-based and prefix-based approaches, where the latter implicitly estimates the specific missing data pattern (i.e., mode sequence), within the given language, according to the prefix observed so far. We illustrate with numerical examples that the proposed approaches can provide desirable performance guarantees.