Zonotopic Recursive Least‐squares Parameter Estimation: Application to Fault Detection

SummaryThe uncertain parameters estimation problem for linear discrete‐time systems modeled in regression form and assuming an unknown but bounded description of the noise, is the main subject of this work. Particularly, zonotopic sets for bounding the parametric uncertainty are considered. Then, a zonotopic recursive least‐squares (ZRLS) estimator is proposed and compared with its stochastic counterpart (RLS), as well as with the set‐membership (SM) approach. Likewise, the parameter estimation problem is addressed from the Bayesian general framework to define the relationship between stochastic and deterministic approaches. Moreover, both ZRLS and SM applications applied to fault detection are assessed taking as a reference the minimum detectable fault in the worst case. Finally, a well‐known quadruple‐tank process is used to illustrate the estimation and fault detection results.