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一类多输入多输出级联系统的边界控制 被引量：1

On the Boundary Control of a Cascade PDE-ODE in Multi-Input and Multi-Output LTI System
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摘要 主要研究了两个反应扩散方程和常微分方程的级联控制系统,在更新原有的Backstepping方法基础上,应用常微分上的线性变换,根据相应条件得到核方程,进而得到核方程的解和控制律.通过逆变换及Lypunov证明闭环系统是指数稳定的. In this paper, the boundary control of a cascade control system is considered, which reflects the reaction-diffusion equation and an ordinary differential equation. The ODE of linear transformation is ap- plied in the updating of the original backstepping transformation method. The kernel functions are obtained based on the corresponding conditions, then the kernel solutions and the control law are obtained. The closed loop system is exponentially stable by proving inverse transformation and Lyapunov function.
作者 甄志远 谢成康 何翠华
机构地区 西南大学数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2016年第5期119-124,共6页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金项目(11301427)
关键词 级联系统 闭环系统 边界控制 稳定性 cascade system closed loop boundary control stability
分类号 O231.2 [理学—运筹学与控制论]
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参考文献12

  • 1KRSTIC M,SMYSHLYAEV A. Boundary Control of PDEs: a Course on Backstepping Design [M]. Philadelphia: SI-AM, 2008: 13-63.
  • 2LIU W J. Boundary Feedback Stabilization of an Unstable Heat Equation [J]. Siam Journal on Control Optimization,2003, 42(3) ; 1033-1043.
  • 3BACCOIL A,PISANO A, ORLOV Y. Boundary Control of Counpled Reaction-Diffusion Processes with Constan Pa-rameters [J]. Automatic, 2015,54: 80 - 90.
  • 4VAZEQUEZ R, KRSTIC M. Maracm Q-Functions and Explicit Kernels for Stabilization of 2X2 Linear Hyperbolic Sys-tems with Consant Coefficients [J]. System & Control Letters, 2014,68: 33 - 42.
  • 5TANG S X,XIE C K. Stabilization for a Coupled PDE-ODE Control System [J], Journal of the Franklin Institute, 2011,348(8): 2142-2155.
  • 6TANG S X,XIE C K. State and Output Feedback Boundary Control for a Coupled PDE-ODE System [J].Systems &-Control Letters, 2011,60(8) : 540 - 545.
  • 7ZHAO A L, XIE C K. Stabilization of a Coupled Linear Plant and Reaction-Diffusion Process [J]. Journal of the FrankinInstitute, 2014,351(2): 857 - 877.
  • 8SUSTO G A,KRSTIC M. Control of PDE-ODE Cascades with Neumann Interconnections [J]. Jounal of the Franklin In-stitute, 2010,347(1): 284-314.
  • 9ZHOU Z C, GUO C L. Stabilization of Linear Heat Equation with a Heat Source at Intermediate Point by Boundary Con- trol[J].Automatica, 2013, 49(2): 448--456.
  • 10ZHOU Z C,XU C. Stabilization of a Second Order ODE-Heat System Coupling at Intermediate Point [J]. Automatic,2015,60: 57-64.

二级参考文献5

  • 1Zhongcheng Zhou,Chunli Guo.Stabilization of linear heat equation with a heat source at intermediate point by boundary control[J]. Automatica . 2012
  • 2Gian Antonio Susto,Miroslav Krstic.Control of PDE–ODE cascades with Neumann interconnections[J]. Journal of the Franklin Institute . 2009 (1)
  • 3S. Tang,C. Xie.Stabilization for a coupled PDE-ODE system with boundary control. Proceedings of the 49th IEEE Conference on Decision and Control . 2010
  • 4Tang, Shuxia,Xie, Chengkang.State and output feedback boundary control for a coupled PDEODE system. Systems and Control Letters . 2011
  • 5KRSTIC M,SMYSHLYAEV A.Boundary Control of PDEs:a Course on Backstepping Design. . 2008

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西南大学学报（自然科学版）
2016年 第5期

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