Control of PDE-ODE cascades with Neumann interconnections
Control of PDE-ODE cascades with Neumann interconnections
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DOI：
10.1016/j.jfranklin.2009.09.005
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发表时间：
2010-02
期刊：
影响因子：
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通讯作者：
Gian Antonio Susto;M. Krstić
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文献类型：
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作者：
Gian Antonio Susto;M. Krstić
我们扩展了最近的几个结果的全状态反馈镇定和状态估计的PDE-ODE级联，其中的PDE是热型或波型，从以前考虑的情况下，其中的互连是Dirichlet型，诺依曼型互连。Neumann型互连将PDE态约束为在PDE-ODE界面处服从Dirichlet边界条件，并采用PDE态的一阶空间导数的边界值作为ODE的输入。除了考虑热ODE和波ODE级联，我们还考虑了一个级联的扩散对流PDE与ODE，对流方向是“远离”的ODE。我们将这种情况称为具有“反对流”的PDE-ODE级联。这种情况是有趣的，不仅因为PDE子系统是不稳定的，但因为控制信号受到竞争的扩散，这是在两个方向上的一维域，和对流，这是在与标准延迟（运输PDE）过程的传播方向相反的方向。我们依赖于扩散过程来传播控制信号通过偏微分方程向常微分方程，以稳定常微分方程。
We extend several recent results on full-state feedback stabilization and state estimation of PDE–ODE cascades, where the PDEs are either of heat type or of wave type, from the previously considered cases where the interconnections are of Dirichlet type, to interconnections of Neumann type. The Neumann type interconnections constrain the PDE state to be subject to a Dirichlet boundary condition at the PDE–ODE interface, and employ the boundary value of the first spatial derivative of the PDE state to be the input to the ODE. In addition to considering heat-ODE and wave-ODE cascades, we also consider a cascade of a diffusion–convection PDE with an ODE, where the convection direction is “away” from the ODE. We refer to this case as a PDE–ODE cascade with “counter-convection.” This case is not only interesting because the PDE subsystem is unstable, but because the control signal is subject to competing effects of diffusion, which is in both directions in the one-dimensional domain, and counter-convection, which is in the direction that is opposite from the propagation direction of the standard delay (transport PDE) process. We rely on the diffusion process to propagate the control signal through the PDE towards the ODE, to stabilize the ODE.