This article studies the problem of prescribed-time constrained tracking control for a class of hyperbolic partial differential equation (PDE) systems with actuator dynamics, which are described by a set of nonlinear ordinary differential equations (ODEs). Since the control input only appears in the ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite challenging. The most important is that for the control of such ODE controlled PDE systems we mainly make the following two contributions: (1) the controlled output of the PDE system tracks the reference signal within the prescribed time; (2) the controlled output and all the actuator states are constrained. It is the first time that such a prescribed-time constrained tracking control problem is addressed for the PDE-ODE coupled system considered in this article. Through rigorous theoretical proof, it is demonstrated that all the system states and control signals are bounded and sufficiently continuous by configuring appropriate design parameters. Finally, the performance is investigated via numerical simulation.

中文翻译：

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一类具有执行器动力学的 2 × 2 双曲 PDE 系统的规定时间约束跟踪控制

本文研究一类目标的规定时间约束跟踪控制问题具有执行器动力学的双曲偏微分方程 (PDE) 系统，由一组非线性常微分方程 (ODE) 描述。由于控制输入仅出现在 ODE 子系统中而不是直接出现在 PDE 子系统的边界上，因此控制任务变得相当具有挑战性。最重要的是，对于此类ODE控制的PDE系统的控制，我们主要做出以下两个贡献：（1）PDE系统的受控输出在规定时间内跟踪参考信号；(2)受控输出和所有执行器状态均受到约束。对于本文考虑的 PDE-ODE 耦合系统，这是第一次解决这种规定时间约束跟踪控制问题。通过严格的理论证明，通过配置适当的设计参数，所有系统状态和控制信号都是有界的且足够连续。最后，通过数值模拟研究其性能。