We present a certainty equivalence-based adaptive boundary control scheme with a regulation-triggered batch least-squares identifier, for a heterodirectional transport partial differential equation-ordinary differential equation (PDE-ODE) system where the transport speeds of both transport PDEs are unknown. We use a nominal controller which is fed piecewise-constant parameter estimates from an event-triggered parameter update law that applies a least-squares estimator to data “batches” collected over time intervals between the triggers. A parameter update is triggered by an observed growth in the norm of the PDE state. The proposed triggering-based adaptive control guarantees: (1) the absence of a Zeno phenomenon; (2) parameter estimates are convergent to the true values in finite time (from most initial conditions); (3) exponential regulation of the plant states to zero. The effectiveness of the proposed design is verified by a numerical example.

中文翻译：

---

具有边界互连的双曲线 PDE-ODE 模型的调节触发自适应控制

我们针对异向传输偏微分方程-常微分方程 (PDE-ODE) 系统提出了一种基于确定性等价的自适应边界控制方案，该方案具有调节触发的批量最小二乘标识符，其中两个传输 PDE 的传输速度未知。我们使用标称控制器，该控制器从事件触发的参数更新法则中获取分段常数参数估计，该法则将最小二乘估计器应用于在触发器之间的时间间隔内收集的数据“批次”。参数更新由观察到的 PDE 状态范数的增长触发。所提出的基于触发的自适应控制保证：(1) 不存在 Zeno 现象；(2) 参数估计在有限时间内（从大多数初始条件开始）收敛到真实值；(3) 植物状态的指数调节为零。通过数值例子验证了所提出设计的有效性。