This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem, an invertible transformation is first introduced to change the system into an observer canonical form, from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

本文研究了一类不确定PDE-ODE级联系统的自适应镇定。值得注意的是，PDE子系统允许未知的控制系数和空间变化的参数，并且仅可以测量其一个边界值。这使得所讨论的系统更加通用和实用，并且控制问题更具挑战性。为了解决该问题，首先引入了可逆变换，将系统更改为观察者规范形式，从中构造了两个滤波器来估计不可测量的状态。然后，通过自适应技术和无限维反步法，构造了一个自适应控制器，该控制器可确保最终闭环系统的所有状态都处于有界状态，而原始系统状态则收敛到零。最后，