Robust fuzzy control subject to state variance and passivity constraints for perturbed nonlinear systems with multiplicative noises

• Published in: ISA transactions Vol. 53; no. 6; pp. 1787 - 1795
• Main Authors: Chang, Wen-Jer, Huang, Bo-Jyun
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.11.2014
• Subjects: Dynamical systems; Fuzzy control; Individual state variance constraint; Mathematical models; Noise; Nonlinear dynamics; Passivity; Passivity constraint; Perturbed nonlinear systems; Robust fuzzy control; Stability; Takagi–Sugeno fuzzy model with multiplicative noises; Variance; Perturbed nonlinear systems; Takagi–Sugeno fuzzy model with multiplicative noises; Individual state variance constraint; Robust fuzzy control; Passivity constraint
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2014.08.016

The multi-constrained robust fuzzy control problem is investigated in this paper for perturbed continuous-time nonlinear stochastic systems. The nonlinear system considered in this paper is represented by a Takagi–Sugeno fuzzy model with perturbations and state multiplicative noises. The multiple performance constraints considered in this paper include stability, passivity and individual state variance constraints. The Lyapunov stability theory is employed to derive sufficient conditions to achieve the above performance constraints. By solving these sufficient conditions, the contribution of this paper is to develop a parallel distributed compensation based robust fuzzy control approach to satisfy multiple performance constraints for perturbed nonlinear systems with multiplicative noises. At last, a numerical example for the control of perturbed inverted pendulum system is provided to illustrate the applicability and effectiveness of the proposed multi-constrained robust fuzzy control method. •The robust and multiple constrained fuzzy control problems are investigated in this paper for perturbed continuous-time nonlinear stochastic systems.•The nonlinear system is constructed by a Takagi–Sugeno fuzzy model with perturbations and state multiplicative noises.•The performance constraints considered in this paper include individual state variance constraint and passivity constraint.•Solving LMI conditions derived in this paper, a parallel distributed compensation based robust fuzzy controller is obtained to satisfy multiple constraints.