Zonotope-based recursive estimation of the feasible solution set for linear static systems with additive and multiplicative uncertainties

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear static models, where both additive and multiplicative uncertainties are treated explicitly. The two recursive algorithms can be differentiated by their ways of processing the data and required computations. The first algorithm, which is referred to as Cone And Zonotope Intersection (CAZI), requires solving linear programming problems at each iteration. The second algorithm, referred to as the Polyhedron And Zonotope Intersection (PAZI), involves linear programming as well as an optimization subject to linear matrix inequalities (LMIs). Both algorithms are capable of providing tight overbounds of the feasible solution set (FSS) in an application to health monitoring of marine engines. Furthermore, PAZI algorithm applied to mini-batches of measurement data leads itself to further analysis of the relation between the estimation results at different iterations. In addition, an example of identifying time-varying parameters is also reported.