Zonotopic observer designs for uncertain Takagi–Sugeno fuzzy systems. (September 2022)

• Record Type: Journal Article
• Authors: Pourasghar, Masoud; Nguyen, Anh-Tu; Guerra, Thierry-Marie
• Is Part Of: Engineering applications of artificial intelligence. Volume 114(2022)
• Publication Date: 2022-09
• Subjects: Takagi–Sugeno fuzzy systems -- Fuzzy observers -- Unmeasured premise variables -- State estimation -- Uncertainty -- Linear matrix inequality (LMI); Engineering -- Data processing -- Periodicals; Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Ingénierie -- Informatique -- Périodiques; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; Artificial intelligence; Engineering -- Data processing; Expert systems (Computer science); Periodicals; 620.00285
• DOI: 10.1016/j.engappai.2022.105126
• Languages: English
• ISSNs: 0952-1976

Abstract

Abstract: This paper addresses the zonotopic observer design for nonlinear systems affected by uncertainties, i.e., state disturbances and measurement noises using Takagi–Sugeno (TS) fuzzy technique. The system uncertainties are considered as unknown but bounded, which are handled via a set-membership framework. For state estimation purposes, we develop an algorithm to recursively compute the zonotope containing the mismatching nonlinear term caused by unmeasured nonlinearities. Then, two methods are proposed to design the zonotopic observer gains. The first method is based on the minimization of the F − radius of zonotopes, for which the membership-function-dependent observer gain must be completely computed online. For the second method, an ℋ ∞ approach is used together with a nonquadratic Lyapunov function to determine the observer gain. Then, the zonotopic observer design is reformulated a convex optimization problem under linear matrix inequalities (LMIs), which can be effectively solved with numerical solvers. An autonomous vehicle application is provided to demonstrate and analyze the effectiveness of both proposed methods.