This study accentuates the intricacies of designing a quantized observer-oriented model reference tracking controller for parabolic non-linear uncertain partial differential equation (PDE) systems with dissipative constraints. To be precise, a PDE-type Luenberger state estimator is incorporated for accessing the states of examined PDE system with high precision. This strategic incorporation empowers the model reference tracking controller with essential state estimations contributing to the realization of targetted state tracking objectives. Furthermore, as a measure to lighten the load on the communication medium, the input signals are quantized through the utilization of logarithmic quantizers before being transmitted to the actuator and a quantized observer-oriented tracking controller is then implemented to counteract and alleviate the consequential effects arising from quantization. Additionally, to attenuate the repercussions made by disturbances in the proposed system design, a dissipative based performance is incorporated. In the interim by applying the theory of Lyapunov’s stability, the adequate constraints for the undertaken system are frameworked in the context of linear matrix inequalities terms. Further, under the lights of established criteria, the gain matrices are reckoned. At the end, two numerical examples along with simulation outcomes are offered with the intent of showcase the applicability and usefulness of devised control.

中文翻译：

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具有耗散约束的抛物线非线性不确定PDE系统的面向观察者的量化跟踪控制设计


这项研究强调了为具有耗散约束的抛物线非线性不确定偏微分方程（PDE）系统设计量化的面向观察者的模型参考跟踪控制器的复杂性。准确地说，采用了 PDE 型 Luenberger 状态估计器，用于高精度地访问所检查的 PDE 系统的状态。这种战略整合为模型参考跟踪控制器提供了基本的状态估计，有助于实现有针对性的状态跟踪目标。此外，作为减轻通信介质负载的措施，输入信号在传输到执行器之前通过使用对数量化器进行量化，然后实施量化的面向观察者的跟踪控制器以抵消和减轻由此产生的后果来自量化。此外，为了减弱所提出的系统设计中的干扰造成的影响，还结合了基于耗散的性能。在此期间，通过应用李亚普诺夫稳定性理论，在线性矩阵不等式项的背景下对所采用的系统进行充分的约束。此外，根据既定标准，计算增益矩阵。最后，提供了两个数值示例以及模拟结果，旨在展示所设计的控制的适用性和有用性。