| 引用本文: | 甄志远,谢成康,司元超,何翠华.二阶抛物系统的边界控制稳定[J].控制理论与应用,2018,35(6):859~867.[点击复制] |
| ZHEN Zhi-yuan,XIE Cheng-kang,SI Yuan-chao,HE Cui-hua.Stabilization of the second order parabolic system by boundary control[J].Control Theory and Technology,2018,35(6):859~867.[点击复制] |
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| 二阶抛物系统的边界控制稳定 |
| Stabilization of the second order parabolic system by boundary control |
| 摘要点击 2218 全文点击 1510 |
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| DOI编号 10.7641/CTA.2017.17047 |
| 2018,35(6):859-867 |
| 中文关键词 边界控制 抛物方程组 后推法 控制律 稳定 |
| 英文关键词 boundary control parabolic equations backstepping control law stability |
| 基金项目 Supported by the National Natural Science Foundation of China (11671326). |
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| 中文摘要 |
| 本文考虑二阶抛物系统的边界控制问题. 系统的状态方程包含了对流和反应扩散项. 通过后推法, 建立了系统
的边界控制律, 并且获得了后推变换核矩阵方程的级数解. 通过后推变换及其逆变换的有界性, 证明了闭环系统的稳定
性. 对一个具体的系统进行了仿真, 结果用图形呈现出来. |
| 英文摘要 |
| Boundary control to stabilize a system of the second order parabolic equations is addressed. The state equation
is a second order parabolic system with an advection and a reaction-diffusion terms. A boundary control law of the system
is established through PDE backstepping. The kernel matrix equation of backstepping transformation is solved, and its
solution is written in the form of series. Stability of the closed loop is shown through boundedness of the backstepping
transformation and its inverse. A specific system is simulated. Simulation results are presented by figures. |