In this paper, the output feedback stabilization of an underactuated chain of scalar hyperbolic systems coupled at one end with a finite-dimensional system is addressed. As encountered in practical applications, only the first PDE subsystem is actuated. The measurements are collocated with the actuation. The proposed approach uses a recursive dynamics interconnection framework. More precisely, we first estimate (delayed) values of the states at each subsystem’s boundaries. Then, we design a state-predictor that gives access to the boundary states’ present and future values. It becomes finally possible to design a state-observer for the entire system. Combining this observer with a stabilizing state-feedback law, we can recursively design an output-feedback control law that stabilizes the whole chain. Some illustrative examples complete the presentation.

在本文中，解决了在一端与有限维系统耦合的标量双曲线系统的欠驱动链的输出反馈稳定问题。在实际应用中，只有第一个 PDE 子系统被驱动。测量与致动并置。所提出的方法使用递归动态互连框架。更准确地说，我们首先估计（延迟）每个子系统边界的状态值。然后，我们设计了一个状态预测器，可以访问边界状态的当前和未来值。最终可以为整个系统设计一个状态观察器。将这个观察器与稳定状态反馈法则相结合，我们可以递归地设计一个稳定整个链的输出反馈控制法则。