论文标题
坦克 - 液体系统的反馈稳定，具有稳健性的壁摩擦
Feedback Stabilization of Tank-Liquid System with Robustness to Wall Friction
论文作者
论文摘要
我们解决了储罐的反馈稳定问题，其中摩擦含有液体，该液体由呈粘性的偏微分方程的粘性圣人系统建模。实现了无泄漏指数的稳定，对壁摩擦力具有稳健性。采用了具有两个不同Lyapunov功能的对照Lyapunov功能（CLF）方法。这些功能确定特定的参数化集，该集合近似状态空间。反馈定律的设计仅基于两个功能之一（即CLF）之一，而另一个功能则用于衍生速度的SUP-NORM的估计值。反馈法不需要了解摩擦系数的确切关系。提供了两个主要结果：第一个交易与速度无关的摩擦系数的特殊情况，而第二个则处理了一般情况。即使在无摩擦情况下，获得的结果也是新的。
We solve the feedback stabilization problem for a tank, with friction, containing a liquid modeled by the viscous Saint-Venant system of Partial Differential Equations. A spill-free exponential stabilization is achieved, with robustness to the wall friction forces. A Control Lyapunov Functional (CLF) methodology with two different Lyapunov functionals is employed. These functionals determine specific parameterized sets which approximate the state space. The feedback law is designed based only on one of the two functionals (which is the CLF) while the other functional is used for the derivation of estimates of the sup-norm of the velocity. The feedback law does not require the knowledge of the exact relation of the friction coefficient. Two main results are provided: the first deals with the special case of a velocity-independent friction coefficient, while the second deals with the general case. The obtained results are new even in the frictionless case.
