Zonotope-based set-membership parameter identification of linear systems with additive and multiplicative uncertainties: A new algorithm

Abstract

In this paper, we develop two zonotope-based set-membership estimation algorithms for identification of time-varying parameters in linear 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 our numerical case studies. Furthermore, PAZI provides an additional opportunity of further analyzing the relation between the estimation results at different iterations. An application to health monitoring of marine engines is considered to demonstrate the utility and effectiveness of the algorithms. (Hao Wang), ilya@umich.edu (Ilya Kolmanovsky), jingsun@umich.edu (Jing Sun).to model reference control [17], [8] and robust MPC [16], and other novel applications (e.g. simultaneous localization and mapping (SLAM) [18] and diabetes treatment [10]). Set-membership techniques for simultaneous input and parameter estimation are developed in [11].

Joint state and parameter estimation based on constrained zonotopes

“…Set-based methods have also been widely used in the parameter identification field as an alternative to stochastic methods, since they are able to provide guaranteed enclosures of the model parameters when the uncertain model parameters have unknown stochastic properties. Zonotopes have been used to approximate the parametric set for discrete-time systems with additive uncertainties in Bravo et al (2006), which was later extended to allow multiplicative uncertainties in Wang et al (2017). However, both methods are applied only to systems described by regression models, and rely on conservative intersections with strips to refine the parametric set.…”

A new kernel RLS algorithm for systems with bounded noise

“…A complete overview of the works achieved in ellipsoidal bounding can be found in the work of Norton. 15 Other families of SM algorithms have also emerged that use orthotope 2,4,16 or zonotope 17 bounding to describe the membership set. String matching algorithms research tool (SMART) algorithms 6,8,18,19 are built based on the OBE family.…”