Further results on the design of a class of discrete‐time set‐valued state estimators

• Published in: International journal of robust and nonlinear control Vol. 32; no. 2; pp. 649 - 668
• Main Authors: Meslem, Nacim, Raïssi, Tarek, Besançon, Gildas
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.01.2022; Wiley
• Subjects: Algorithms; Automatic; Constraints; Cost function; Engineering Sciences; Estimators; interval analysis; Linear systems; nonlinear optimization; Optimization; set‐membership estimation; State estimation; uncertain systems; zonotopic set computation
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5841

In this work, two improvements are proposed for a class of interval‐based state estimators applied to discrete‐time uncertain linear systems subject to additive bounded process and measurement uncertainties. First, we propose to compute the observer gain as a solution of an off‐line constrained nonlinear optimization problem, where the cost function depends on the estimation error width and the constraints ensure the invariance of the estimation error set. Second, to obtain tighter state enclosures, we propose to apply zonotope set computation instead of interval analysis to design a new set‐valued state estimation algorithm. Through simulations, we highlight the interest of the proposed technical improvements.