|
|
- 2017
一类耦合反应扩散系统的边界控制
|
Abstract:
利用Backstepping的方法对系统内部有热源的耦合线性方程组反应扩散系统进行研究，推导出了这一类耦合系统的核方程，并且证明了闭环系统的稳定性.
This paper uses the backstepping method to study a class of PDE-ODE coupled systems, the focus being placed on the reaction-diffusion system of coupled linear equations with a heat source. The existence of the kernel function is shown, and the stability of the closed loops is achieved
| [1] | KRSTIC M, SMYSHLYAEV A. Boundary Control of PDEs: A Course on Backstepping Designs[M]. Philadelphia: SIAM, 2008: 1-202. |
| [2] | ZHANG X, ZUAZUA E. Polynomial Decay and Control of a 1-d Hyperbolic-Parabolic Coupled System[J]. Journal of Differential Equations, 2004, 204(2): 380-438. DOI:10.1016/j.jde.2004.02.004 |
| [3] | ZHAO A, XIE C. Stabilization of a Coupled Linear Plant and Reaction-Diffusion Process[J]. Journal of the Frankin Institute, 2014, 351(2): 857-877. DOI:10.1016/j.jfranklin.2013.09.012 |
| [4] | ZHANG X, ZUAZUA E. Control Observation and Polynomial Decay for a Coupled Heat-Wave System[J]. Comptes Rendus Mathematique, 2003, 336(10): 823-828. DOI:10.1016/S1631-073X(03)00204-8 |
| [5] | TANG S, XIE C. Stabilization for Acoupled PDE-ODE System with Boundary Control[J]. Journal of the Franklin Institute, 2011, 348(1): 2142-2155. |
| [6] | TANG S, XIE C. Stabilization for a Coupled PDE-ODE Control System[J]. Journal of the Franklin Institute, 2011, 348(8): 2142-2155. DOI:10.1016/j.jfranklin.2011.06.008 |
| [7] | TANG S, XIE C. Stabilization for a Coupled PDE-ODE System with Boundary Control[C] //IEEE Conference on Decision and Control. New York: IEEE Press, 2011. |
| [8] | SUSTO G A, KRSTIC M. Control of PDE-ODE Cascades with Neumanninter Connections[J]. Journal of the Franklin Institute, 2010, 347(1): 284-314. DOI:10.1016/j.jfranklin.2009.09.005 |
| [9] | BEKIARIS-LIBERIS N, KRSTIC M. Compensating Distributed Effect of Diffusion and Counter-Convection in Multi-Input and Multi-Output LTI Systems[J]. IEEE Transactions on Automatic Control, 2011, 56(3): 637-642. DOI:10.1109/TAC.2010.2091187 |
| [10] | ZHANG X, ZUAZUA E. Polynomial Decay and Control of a 1-d Model for Fluid-Structure Interaction[J]. Comptes Rendus Mathematique, 2003, 336(9): 745-750. DOI:10.1016/S1631-073X(03)00169-9 |
| [11] | SMYSHLYAEV A, KRSTIC M. Adaptive Control of Parabolic PDEs[M]. Princenton: Princeton University Press, 2010: 123-125. |
