一类空间非因果关系反应扩散方程的边界控制

郭春丽

doi:10.13718/j.cnki.xsxb.2018.09.005

西南师范大学学报(自然科学版)

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一类空间非因果关系反应扩散方程的边界控制

郭春丽. 一类空间非因果关系反应扩散方程的边界控制[J]. 西南师范大学学报(自然科学版), 2018, 43(9): 22-29. doi: 10.13718/j.cnki.xsxb.2018.09.005

引用本文:

郭春丽. 一类空间非因果关系反应扩散方程的边界控制[J]. 西南师范大学学报(自然科学版), 2018, 43(9): 22-29. doi: 10.13718/j.cnki.xsxb.2018.09.005

GUO Chun-li. Stabilization of a Spatially Non-Causal Reaction-Diffusion Equation by Boundary Control[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(9): 22-29. doi: 10.13718/j.cnki.xsxb.2018.09.005

Citation:

GUO Chun-li. Stabilization of a Spatially Non-Causal Reaction-Diffusion Equation by Boundary Control[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(9): 22-29. doi: 10.13718/j.cnki.xsxb.2018.09.005

一类空间非因果关系反应扩散方程的边界控制

郭春丽

四川文理学院数学学院, 四川达州 635000

Stabilization of a Spatially Non-Causal Reaction-Diffusion Equation by Boundary Control

GUO Chun-li

School of mathematics, School of Sichuan University of Arts and Science, Dazhou Sichuan 635000, China

摘要: 运用Backstepping方法研究了一类空间非因果关系的反应扩散方程的稳定性问题，该系统的温度与整个空间有关系，而不是仅仅与空间中的某一点有关，因此，给控制器的设计带来了难度.为设计反馈控制器，首先，选用边界反馈控制的Backstepping方法进行设计；其次，在设计过程中增加核函数个数，引入改进后的Volterra型积分变换，再采用求解偏微分方程的变量分离法求解出核函数；最后，找到Volterra变换的逆变换，利用Volterra变换及其逆变换的有界性，可证明控制器的有效性.
- 反应扩散方程 /
- Volterra变换 /
- 稳定性 /
- 边界控制
Abstract: Stabilization of a reaction-diffusion equation, in which the heat source depends on the temperature of the whole space, is considered by boundary control. The system is more complicated. For the new system, a new Volterra transformation is introduced, in which there are two kernels. Through a solution of separated variables, the exact solutions of kernels are obtained, and a control law is obtained specifically. The inverse transformation is derived, and stability of the closed loop system established via the boundedness of transformation and the inverse transformation.
- reaction-diffusion equation /
- Volterra transformation /
- stability /
- boundary control .

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一类空间非因果关系反应扩散方程的边界控制

郭春丽

四川文理学院数学学院, 四川达州 635000

收稿日期: 2016-11-30

关键词:

摘要: 运用Backstepping方法研究了一类空间非因果关系的反应扩散方程的稳定性问题，该系统的温度与整个空间有关系，而不是仅仅与空间中的某一点有关，因此，给控制器的设计带来了难度.为设计反馈控制器，首先，选用边界反馈控制的Backstepping方法进行设计；其次，在设计过程中增加核函数个数，引入改进后的Volterra型积分变换，再采用求解偏微分方程的变量分离法求解出核函数；最后，找到Volterra变换的逆变换，利用Volterra变换及其逆变换的有界性，可证明控制器的有效性.