Robust H_∞ Control for Nonlinear Hyperbolic PDE Systems Based on the Polynomial Fuzzy Model.

Area of Science:

• Control Theory
• Nonlinear Systems
• Partial Differential Equations (PDEs)

Background:

• Nonlinear distributed parameter systems described by hyperbolic PDEs pose significant control challenges.
• Existing stabilization methods often lack robustness or are overly conservative.

Purpose of the Study:

• To develop an H_∞ stabilization method for nonlinear hyperbolic PDE systems.
• To propose a polynomial fuzzy controller and associated stabilization conditions.

Main Methods:

• Identification of hyperbolic PDE systems as polynomial fuzzy PDE systems.
• Development of a homogeneous polynomial Lyapunov functional and spatial derivative sum-of-squares (SDSOS) stabilization condition.
• Design of a recursive algorithm for finding feasible solutions.

Main Results:

• A novel SDSOS exponential stabilization condition is proposed for the identified polynomial fuzzy PDE systems.
• A relaxed H_∞ stabilization condition is introduced to reduce conservatism.
• The method's effectiveness is demonstrated on a nonisothermal plug-flow reactor (PFR).

Conclusions:

• The proposed polynomial fuzzy control strategy effectively achieves H_∞ stabilization for nonlinear hyperbolic PDE systems.
• The developed SDSOS condition and recursive algorithm provide a feasible and less conservative approach.
• The PFR case study validates the practical applicability of the method.