Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints

• Published in: IEEE transactions on cybernetics Vol. 51; no. 9; pp. 4673 - 4684
• Main Authors: Nguyen, Anh-Tu, Coutinho, Pedro, Guerra, Thierry-Marie, Palhares, Reinaldo, Pan, Juntao
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Automatic; Constraints; Control design; Control stability; Control systems; Control theory; Controllers; Design optimization; Discrete time systems; Engineering Sciences; Feedback control; Fuzzy control; Fuzzy Lyapunov functions; fuzzy output-feedback control; Fuzzy systems; input constraints; Liapunov functions; Linear matrix inequalities; Lyapunov methods; Nonlinear control; Nonlinear systems; Nonlinearity; Output feedback; Stability analysis; Symmetric matrices; Takagi–Sugeno (TS) fuzzy systems; "Nonlinear systems"; "Lyapunov methods"; "Control design"; "Symmetric matrices"; "Stability analysis"; "Fuzzy control"
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2020.3009128

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected . The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.