Dual-Mode Robust Fuzzy Model Predictive Control of Time-Varying Delayed Uncertain Nonlinear Systems With Perturbations

• Published in: IEEE transactions on fuzzy systems 2023-07, Vol.31 (7), p.1-15
• Main Authors: Guo, Xuyang, Wang, Zhuping, Zhang, Changzhu, Zhang, Hao, Huang, Chao
• Format: Article
• Language: English
• Subjects: Algorithms; Alternative optimization; bilinear matrix inequalities; Computational modeling; Constraints; Control algorithms; Fuzzy control; Fuzzy systems; lyapunov-razumikhin; Nonlinear systems; Optimal control; Optimization; Parameter uncertainty; Performance degradation; Perturbation; Predictive control; Robust control; robust fuzzy model predictive control; time-varying delay; Time-varying systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3220960

For time-varying delayed nonlinear systems with parameter uncertainties and persistent disturbances, an online and an offline robust fuzzy model predictive control (RFMPC) algorithms are proposed in this paper. Both methods guarantee the input-to-state stability (ISS) of the system. Furthermore, a novel alternative optimization (AOP) approach and a dual-mode OP/AOP strategy are proposed to prevent the performance deterioration of the online optimal control (OP) approach due to the challenges in addressing the bilinear matrix inequality (BMI) constraints. With the established AOP and dual-mode OP/AOP techniques, the optimization problem constrained by BMIs is transformed into convex, and a significantly more precise approximation of the ellipsoidal minimal robust positively invariant (EmRPI) set can be calculated. Besides, the system can eventually converge into a more compact ellipsoidal set. These two alternative optimization methods can be easily extended to various nonlinear systems. A numerical example and a continuous-time stirring tank (CSTR) example are provided to validate the effectiveness and advantages of the established methodologies.