This paper is devoted to the adaptive stabilization for uncertain hyperbolic PDE-ODE cascade systems. Remarkably, unknown spatially varying and unknown constant parameters exist in the PDE and ODE subsystems, respectively. This brings essential difficulties in the design of compensator and boundary controller, and in the involved performance analysis. To solve the control problem, an infinite-dimensional backstepping transformation (simplified as IDBT) and its inverse are first introduced to change the original system into a new system (called target system). Then, a state-feedback boundary controller is constructed for the target system by incorporating the adaptive technique based on projection operator, which can guarantee the desirable stability of the resulting closed-loop system. Finally, a simulation example is provided to illustrate the effectiveness of the proposed adaptive controller.

中文翻译：

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不确定双曲 PDE-ODE 级联系统的自适应镇定

本文致力于不确定双曲 PDE-ODE 级联系统的自适应镇定。值得注意的是，PDE 和 ODE 子系统中分别存在未知的空间变化和未知的常数参数。这给补偿器和边界控制器的设计以及所涉及的性能分析带来了本质上的困难。为解决控制问题，首先引入无限维反步变换（简称IDBT）及其逆变换，将原系统变为新系统（称为目标系统）。然后，结合基于投影算子的自适应技术为目标系统构建状态反馈边界控制器，以保证所得闭环系统的理想稳定性。最后，