N个互联的n+m阶双曲PDE系统构成的欠驱动网络的输出反馈镇定
Output-feedback stabilization of an underactuated network of N interconnected n + m hyperbolic PDE systems
AI总结：
针对仅单端驱动、测量位于另一端的N个n+m阶异向双曲PDE子系统链式欠驱动网络，提出含新型积分变换的输出反馈镇定方法，结合子系统性质递归设计控制器与观测器，经仿真验证有效。
摘要：
本文详细阐述了一种输出反馈镇定控制律的设计方法，该控制律针对由N个子系统构成的欠驱动网络，每个子系统包含n+m个通过边界互联的异向线性一阶双曲偏微分方程（PDE）。该网络呈链式结构，仅其中一个子系统受驱动，可用测量值位于链的另一端。所提方法引入了一类新型积分变换，用于处理不同子系统中的域内耦合，同时保证控制输入与各子系统之间存在“清晰驱动路径”。由此可推导每个子系统的若干核心性质：输出轨迹跟踪、输入-状态稳定性以及可预测性（即设计状态预测器的可能性）。我们结合这些性质递归设计了镇定状态反馈控制器，随后设计了可重构状态延迟值的状态观测器，将该观测器与状态反馈控制律结合，得到输出反馈控制器。仿真结果验证了所提方法的有效性。
英文摘要：
In this article, we detail the design of an output feedback stabilizing control law for an underactuated network of N subsystems of n + m heterodirectional linear first-order hyperbolic Partial Differential Equations interconnected through their boundaries. The network has a chain structure, as only one of the subsystems is actuated. The available measurements are located at the opposite extremity of the chain. The proposed approach introduces a new type of integral transformation to tackle in-domain couplings in the different subsystems while guaranteeing a ''clear actuation path'' between the control input and the different subsystems. Then, it is possible to state several essential properties of each subsystem: output trajectory tracking, input-to-state stability, and predictability (the possibility of designing a state prediction). We recursively design a stabilizing state-feedback controller by combining these properties. We then design a state-observer that reconstructs delayed values of the states. This observer is combined with the state-feedback control law to obtain an output-feedback controller. Simulations complete the presentation.
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