We investigate asymptotically stabilisation for the cascaded system of a nonlinear ODE and a wave PDE with damping terms by a predictor control. Based on the backstepping transformations, the cascaded system is transferred to a target system. Further, a predictor control is designed. It is proved that the target system is asymptotically stable by using a Lyapunov functional. Further the stability of the original system under the proposed control law is equivalent to that of the target system. An example is given to illustrate the validity of the proposed method.

中文翻译：

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具有阻尼项的非线性 ODE 和波 PDE 级联系统的稳定性

我们通过预测器控制研究非线性 ODE 和具有阻尼项的波 PDE 的级联系统的渐近稳定性。基于反步变换，级联系统被转移到目标系统。此外，还设计了预测器控制。利用Lyapunov泛函证明了目标系统是渐近稳定的。此外，在提出的控制律下，原系统的稳定性与目标系统的稳定性相同。给出一个例子来说明所提出方法的有效性。