Control of 1D parabolic PDEs with Volterra nonlinearities, Part II: Analysis

被引：55

作者：

Vazquez, Rafael ^{[2
]}

Krstic, Miroslav ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA

[2] Univ Seville, Dept Ingn Aeroespacial, Seville 41092, Spain

来源：

AUTOMATICA | 2008年 / 44卷 / 11期

关键词：

Distributed parameter systems; Stabilization; Nonlinear control; Feedback linearization; Partial differential equations; Lyapunov function; Boundary conditions;

D O I：

10.1016/j.automatica.2008.04.007

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For a class of stabilizing boundary controllers for nonlinear 1D parabolic PDEs introduced in a companion paper, we derive bounds for the gain kernels of our nonlinear Volterra controllers, Prove the convergence of the series in the feedback laws, and establish the stability properties of the closed-loop system. We show that the state transformation is at least locally invertible and include an explicit construction for computing the inverse of the transformation. Using the inverse, we show L-2 and H-1 exponential stability and explicitly construct the exponentially decaying closed-loop solutions. We then illustrate the theoretical results on an analytically tractable example. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2791 / 2803

页数：13

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