Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system
Backstepping boundary stabilization and state estimation of a 2 × 2 linear hyperbolic system
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DOI：
10.1109/cdc.2011.6160338
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
R. Vázquez;M. Krstić;J. Coron
中科院分区：
文献类型：
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作者：
R. Vázquez;M. Krstić;J. Coron
我们考虑具有空间变化系数的一阶双曲线性偏微分方程 2×2 系统的边界稳定和状态估计问题。首先，我们设计了一种仅在域一端驱动的全状态反馈律，并证明了闭环系统的指数稳定性。然后，我们构造一个并置边界观测器，它只需要在受控端进行测量，并证明观测器估计的收敛性。两个结果相结合以获得并置的输出反馈定律。反步法用于获取控制核和观察核。核是一阶双曲线性 PDE 的 4 × 4 系统的解，具有 Goursat 类型的空间变化系数，其适定性已显示。
We consider the problem of boundary stabilization and state estimation for a 2×2 system of first-order hyperbolic linear PDEs with spatially varying coefficients. First, we design a full-state feedback law with actuation on only one end of the domain and prove exponential stability of the closed-loop system. Then, we construct a collocated boundary observer which only needs measurements on the controlled end and prove convergence of observer estimates. Both results are combined to obtain a collocated output feedback law. The backstepping method is used to obtain both control and observer kernels. The kernels are the solution of a 4 × 4 system of first-order hyperbolic linear PDEs with spatially varying coefficients of Goursat type, whose well-posedness is shown.