Polynomial Fuzzy Observer-Based Feedback Control for Nonlinear Hyperbolic PDEs Systems
针对非线性双曲型偏微分方程系统，建立了多项式模糊模型，并设计了基于观测器的反馈控制器，通过空间导数平方和条件实现指数稳定，最后用数值例子验证了有效性。
This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler's homogeneous theorem, Lyapunov-Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results.