This article develops a robust adaptive boundary output regulation approach for a class of complex anticollocated hyperbolic partial differential equations subjected to multiplicative unknown faults in both the boundary sensor and actuator. The regulator design is based on the internal model principle, which amounts to stabilize a coupled cascade system, which consists of a finite-dimensional internal model driven by a hyperbolic distributed parameter system (DPS). To this end, a systematic sliding mode equipped with a backstepping approach is developed such that the robust state feedback control can be realized. Moreover, since the available information is a faulty boundary measurement at the right side point, state estimation is required. However, due to the presence of boundary unknown faults, we need to solve an issue of joint fault-state estimation. Restrictive persistent excitation conditions are usually required to guarantee the exact estimation of faults but are unrealistic in practice. To this end, a novel concurrent learning (CL) adaptive observer is proposed so that exponential convergence is obtained. It is the first time that the spirit of CL is introduced to the field of DPSs. Consequently, the observer-based adaptive boundary fault tolerant control scheme is developed, and rigorous theoretical analysis is given such that the exponential output regulation can be achieved. Finally, the effectiveness of the proposed methodology is demonstrated via comparative simulations.

中文翻译：

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双曲分布参数系统的并发学习鲁棒自适应容错边界调节。

本文针对一类复杂的反并置双曲偏微分方程开发了一种稳健的自适应边界输出调节方法，该方程在边界传感器和执行器中都受到乘法未知故障的影响。稳压器设计基于内部模型原理，相当于稳定耦合级联系统，该系统由双曲线分布参数系统 (DPS) 驱动的有限维内部模型组成。为此，开发了一种配备反步法的系统滑动模式，从而可以实现鲁棒状态反馈控制。此外，由于可用信息是右侧点的错误边界测量，因此需要进行状态估计。但由于边界未知故障的存在，我们需要解决联合故障状态估计的问题。通常需要限制性持续激励条件来保证对故障的准确估计，但在实践中是不现实的。为此，提出了一种新的并发学习 (CL) 自适应观察器，以便获得指数收敛。这是第一次将CL精神引入DPS领域。因此，开发了基于观测器的自适应边界容错控制方案，并给出了严格的理论分析，从而实现指数输出调节。最后，通过比较模拟证明了所提出方法的有效性。为此，提出了一种新的并发学习 (CL) 自适应观察器，以便获得指数收敛。这是第一次将CL精神引入DPS领域。因此，开发了基于观测器的自适应边界容错控制方案，并给出了严格的理论分析，从而实现指数输出调节。最后，通过比较模拟证明了所提出方法的有效性。为此，提出了一种新的并发学习 (CL) 自适应观察器，以便获得指数收敛。这是第一次将CL精神引入DPS领域。因此，开发了基于观测器的自适应边界容错控制方案，并给出了严格的理论分析，从而实现指数输出调节。最后，通过比较模拟证明了所提出方法的有效性。并给出了严格的理论分析，使得可以实现指数输出调节。最后，通过比较模拟证明了所提出方法的有效性。并给出了严格的理论分析，使得可以实现指数输出调节。最后，通过比较模拟证明了所提出方法的有效性。