Path-dependent controller and estimator synthesis with robustness to delayed and missing data

This paper presents path-dependent feedback controllers and estimators with bounded tracking and estimation error guarantees for discrete-time affine systems with time-varying delayed and missing data, where the set of all temporal patterns for the missing or delayed data is constrained by a fixed-length language. In particular, we propose two controller/estimator synthesis approaches based on output feedback and output error feedback parameterizations such that the tracking or estimation errors satisfy a property known as equalized recovery, where the errors are guaranteed to satisfy a recovery level at the start and the end of a finite time horizon, but may temporarily increase (by a bounded amount) within the horizon. To achieve this, we introduce a mapping of the fixed-length delayed/missing data language onto a reduced event-based language, and present designs with feedback gain matrices that adapt based on the observed path in the reduced language, resulting in improved performance. Furthermore, we propose a word observer that finds the set of words (i.e., the delayed/missing data patterns) in the original fixed-length language that are compatible with the observed path. The effectiveness of the proposed approaches when compared to existing approaches is demonstrated using several illustrative examples.