Sliding Mode Control of Markovian Jump Fuzzy Systems: A Dynamic Event-Triggered Method

• Published in: IEEE transactions on fuzzy systems Vol. 29; no. 10; pp. 2902 - 2915
• Main Authors: Cao, Zhiru, Niu, Yugang, Lam, Hak-Keung, Zhao, Jiancong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Communication networks; Control stability; Controllers; Detectors; Dynamic event-triggered mechanism (DETM); Fuzzy control; Fuzzy systems; Heuristic algorithms; Markovian jump systems (MJSs); Optimization; Sliding mode control; sliding mode control (SMC); Stability analysis; Symmetric matrices; T–S fuzzy model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2020.3009729

In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T-S fuzzy model. First, in order to reduce the frequency of state transmission for alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method.