Stabilization of a spatially non‐causal reaction–diffusion equation by boundary control
Stabilization of a spatially non‐causal reaction–diffusion equation by boundary control
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DOI：
10.1002/rnc.2864
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发表时间：
2014-01
影响因子：
3.9
通讯作者：
C. Guo;C. Xie;C. Zhou
中科院分区：
文献类型：
--
作者：
C. Guo;C. Xie;C. Zhou
考虑了热源依赖于整个空间温度的反应扩散方程的边界控制问题。引入了一种新的回溯变换，其中有两个核。通过一系列的数学技巧，得到了核的精确解，并具体地得到了控制律。推导了系统的逆变换，建立了闭环系统的稳定性。仿真结果表明，闭环系统是稳定的。版权所有©2012 John Wiley & Sons， Ltd。
Stabilization of a reaction–diffusion equation, in which the heat source depends on the temperature of the whole space, is considered by using boundary control. A new backstepping transformation is introduced, in which there are two kernels. Through a series of mathematical tricks, 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. Simulation results show that the closed loop system is stable. Copyright © 2012 John Wiley & Sons, Ltd.