H Fuzzy Observer-Based Control for a Class of Nonlinear Distributed Parameter Systems With Control Constraints

• Published in: IEEE transactions on fuzzy systems Vol. 16; no. 2; pp. 502 - 516
• Main Authors: Wu, Huai-Ning, Li, Han-Xiong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bilinear matrix inequality (BMI); control constraints; Control design; Control systems; Differential equations; distributed parameter systems; Dynamical systems; Fuzzy; Fuzzy control; Fuzzy logic; Fuzzy set theory; Fuzzy systems; Galerkin's method; H _{\infty} control; Inequality; Linear matrix inequalities; Moment methods; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear dynamics; Nonlinearity; Partial differential equations; Studies
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2007.896351

An H infin fuzzy observer-based control design is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems with control constraints, for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. In the proposed control scheme, Galerkin's method is initially applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T-S fuzzy model, a fuzzy observer-based controller is developed to stabilize the nonlinear PDE system and achieve an optimized H infin disturbance attenuation performance for the finite-dimensional slow system, while control constraints are respected. The outcome of the H infin fuzzy observer-based control problem is formulated as a bilinear matrix inequality (BMI) optimization problem. A local optimization algorithm that treats the BMI as a double linear matrix inequality is presented to solve this BMI optimization problem. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness.