Stable adaptive probabilistic Takagi–Sugeno–Kang fuzzy controller for dynamic systems with uncertainties

• Published in: ISA transactions 2020-03, Vol.98, p.271-283
• Main Authors: Shaheen, Omar, El-Nagar, Ahmad M., El-Bardini, Mohammad, El-Rabaie, Nabila M.
• Format: Article
• Language: English
• Subjects: Lyapunov theory; Probabilistic fuzzy system; Probabilistic TSK fuzzy controller; Uncertain systems
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2019.08.035

In this study, an adaptive probabilistic Takagi–Sugeno–Kang fuzzy PID (APTSKF-PID) scheme is developed to control nonlinear systems. The proposed controller merges the features of the TSK fuzzy logic system, which possess a superior performance in system size and learning accuracy than the Mamdani-type fuzzy systems and the probabilistic processing method in nonlinear control, which handles the system uncertainties. To achieve controlled system stability, Lyapunov function is used for tuning the controller parameters. Tuning the probability parameters provides an extra degree of flexibility in controller design and improves the control performance. Furthermore, to ensure the effectiveness of the developed scheme for engineering applications, the proposed control technology is introduced to control nonlinear dynamical plants and its performance is compared with existing schemes. Simulation tasks indicate that the efficiency of APTSKF-PID scheme has high superiority over the other controller for external disturbances, random noise and a large scope of system uncertainties. •An adaptive probabilistic TSK fuzzy controller is introduced.•The proposed controller combines the advantages of TSK fuzzy and probabilistic theory.•The controller parameters are updated on-line based on the Lyapunov theorem.