This paper considers general heterodirectional linear hyperbolic PDEs with boundary actuation and collocated measurement, that are bidirectionally coupled with nonlinear ODEs at the unactuated boundary. An output feedback regulator is designed to have the control output track a reference in the presence of disturbances, with a nonlinear signal model generating the reference and the disturbances. This leads to new challenges for both the observer and controller design. The regulator design makes use of results from output regulation theory for nonlinear lumped-parameter and distributed-parameter systems. The derivation of the state feedback regulator requires solving a new type of regulator equations, which consist of a Cauchy problem for linear and semilinear hyperbolic PDEs. A key component of the novel observer design is a nonlinear retarded observer for a finite-dimensional subsystem. Both the controller and the observer design are systematic in nature and derived in several successive steps, that include backstepping transformations and, most notably, predictions of PDE and ODE states. The latter are shown to be the unique solution of general nonlinear Volterra integro-differential equations. Combining the observer with the state feedback regulator is proven to achieve output regulation for the closed-loop system. A numerical example illustrates and confirms the theoretical results.

本文考虑了具有边界驱动和并置测量的一般异向线性双曲 PDE，它们在未驱动边界处与非线性 ODE 双向耦合。输出反馈调节器旨在让控制输出在存在干扰的情况下跟踪参考，非线性信号模型生成参考和干扰。这给观察者和控制器设计带来了新的挑战。调节器设计利用了非线性集中参数和分布参数系统的输出调节理论的结果。状态反馈调节器的推导需要求解一种新型调节器方程，其中包括线性和半线性双曲 PDE 的柯西问题。新颖的观察器设计的一个关键组成部分是有限维子系统的非线性延迟观察器。控制器和观察器的设计本质上都是系统化的，并且是通过几个连续的步骤得出的，其中包括反推变换，最值得注意的是，PDE 和 ODE 状态的预测。后者被证明是一般非线性 Volterra 积分微分方程的唯一解。事实证明，将观测器与状态反馈调节器相结合可以实现闭环系统的输出调节。一个数值例子说明并证实了理论结果。PDE 和 ODE 状态的预测。后者被证明是一般非线性 Volterra 积分微分方程的唯一解。事实证明，将观测器与状态反馈调节器相结合可以实现闭环系统的输出调节。一个数值例子说明并证实了理论结果。PDE 和 ODE 状态的预测。后者被证明是一般非线性 Volterra 积分微分方程的唯一解。事实证明，将观测器与状态反馈调节器相结合可以实现闭环系统的输出调节。一个数值例子说明并证实了理论结果。