A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws
A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws
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DOI：
10.1109/cdc.2004.1428994
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
J. Coron;B. d'Andréa-Novel;G. Bastin
中科院分区：
文献类型：
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作者：
J. Coron;B. d'Andréa-Novel;G. Bastin
我们提出了一个严格的李雅普诺夫函数的双曲型系统的守恒律，可以对角化与黎曼不变量。该李雅普诺夫函数的时间导数可以通过适当地选择边界条件来严格确定为负。它示出，派生的边界控制允许保证状态的局部收敛到一个所需的设定点。此外，控制可以被实现为仅在边界处测量的状态的反馈。以水平明渠的水位流量调节为例，说明了控制设计方法。
We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalised with Riemann invariants. The time derivative of this Lyapunov function can be made strictly definite negative by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with a hydraulic application, namely the level and flow regulation in a horizontal open channel.