Dirichlet boundary stabilization of unstable mixed parameter systems
Dirichlet boundary stabilization of unstable mixed parameter systems
复制标题
不稳定混合参数系统的狄利克雷边界稳定
DOI：
10.1109/mcsi.2014.14
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Hideki Sano
中科院分区：
文献类型：
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作者：
Ryuichi Ashino;Takeshi Mandai;and Akira Morimoto;Jun Sekine;Hideki Sano
本文研究了由一维传输扩散过程和不稳定常微分方程(ODE)对象组成的级联系统的有限维镇定问题，其中ODE对象与传输扩散过程通过过滤器相连。整个系统的输入只是输运扩散过程的Dirichlet边界输入，输出是过程域边界上的Dirichlet数据和常微分方程对象的输出。本文利用最新的方法证明了具有这种输入和输出的一维输运扩散过程可以表示为具有γ有界输出算子和直接反馈项的系统。结果表明，在常微分方程对象能控能观的假设下，当上述滤波器为残差模式滤波器时，整个系统的有限维模型变得能控和能观。这一事实使我们能够利用RMF方法来构造有限维镇定控制器。
In this paper, we study the finite-dimensional stabilization problem of the cascade consisting of the one-dimensional transport-diffusion process and an unstable Ordinary Differential Equation (ODE) plant, where the ODE plant is connected with the transport-diffusion process through a filter. The input to the whole system is only Dirichlet boundary input to the transport diffusion process, and the outputs are the Dirichlet data at the boundary of process domain and the output from the ODE plant. In this paper, we use the latest method and show that the one-dimensional transport-diffusion process with such input and output can be formulated as a system with Aγ-bounded output operator and direct feed through term. It is shown that, under the assumption that the ODE plant is controllable and observable, the finite-dimensional model of the whole system becomes controllable and observable, when the filter mentioned above is a Residual Mode Filter (RMF). This fact enables us to construct a finite-dimensional stabilizing controller by using an RMF approach.