Robust H∞Control for Nonlinear Hyperbolic PDE Systems Based on the Polynomial Fuzzy Model
In this article, the H∞ stabilization problem for a class of nonlinear hyperbolic PDEs modeled by the polynomial fuzzy PDE model is addressed.
Fig. 2.Flowchart for the recursive SOS algorithm.
Technology Overview
In this article, based on Euler’s homogeneous function theorem and the proposed HPLF, an H∞ SDSOS exponential stabilization condition without the assumption in common use is proposed. In addition, a recursive algorithm is developed to figure out the feasible solution for the proposed SDSOS stabilization condition. Two cases of nonisothermal PFRs are illustrated to demonstrate the feasibility and effectiveness of the proposed results.
Applications & Benefits
In further investigation, based on the proposed design procedure, we will explore the piecewise stabilization problem for the semilinear parabolic PDE systems via a finite number of pointwise actuators and sensors. The proposed method will also be used for a real model, such as the FitzHugh–Nagumo equation or the Fisher equation.
Abstract：
This article addresses the H ∞ stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order hyperbolic PDE systems are identified as a polynomial fuzzy PDE system and the polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing the proposed homogeneous polynomial Lyapunov functional, Euler's homogeneous function theorem, and the proposed theorems, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. In addition, a recursive algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. Furthermore, in order to reduce the conservatism of the proposed results, a relaxed H ∞ stabilization condition for the polynomial fuzzy PDE system is provided. Finally, the nonisothermal plug-flow reactor (PFR) is used to demonstrate the effectiveness and feasibility of the proposed method.
Robust H∞Control for Nonlinear Hyperbolic PDE Systems Based on the Polynomial Fuzzy Model
Author：Tsai S.-H., Wang J.-W., Song E.-S., Lam H.-K.
Year：2021
Source publication：IEEE Transactions on Cybernetics Volume: 51 Issue: 7
Subfield Highest percentage：99% Control and Systems Engineering #1/260