SOS-based Stability Analysis and Controller Design for Polynomial Partial Differential Equation Systems

• Main Authors: Chih-Yang Jen, 任智揚
• Other Authors: Shun-Hung Tsai
• Format: Others
• Language: en_US
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/8eu36c

碩士 === 國立臺北科技大學 === 自動化科技研究所 === 105 === In this thesis, the problems of controller design and stability analysis for partial differential equations (PDEs) are investigated. Three main research topics are provided in this thesis. Firstly, the first order hyperbolic PDE systems are identified as the polynomial fuzzy PDE system. In addition, a polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing polynomial Lyapunov-Krasvoskii function, and Eulers homogeneous relation, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. Furthermore, an algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. In second part, the sampled-data control problem for the first order hyperbolic PDE system is explored for reducing the implementation cost. In third part, two cases of polynomial fuzzy controllers, which is either with the spatial differential term or not, are considered the problems of performance and the stability for parabolic PDE systems are addressed. Lastly, the nonisothermal plug-flow reactor (PFR) and some numerical examples are illustrated to show the feasibility and validity of the proposed polynomial fuzzy controller and the stabilization conditions.