This paper is concerned with the cooperative output regulation problem for a network of agents with different dynamics described by parabolic PDEs subject to spatially- and time-varying parameters. Firstly, a networked controller is designed achieving output synchronization for identical finite-dimensional reference models, which deliver the state of the global reference model required for the synchronization to the parabolic agents. The latter can be subject to local disturbances acting in-domain, on all boundaries and on the anti-collocated output to be controlled. The cooperative output regulation problem is solved by designing local output feedback regulators for the parabolic agents. This requires the solution of time-varying regulator equations and the design of disturbance observers for parabolic systems with spatially- and time-varying coefficients. For this, a systematic backstepping approach is provided and it is shown that cooperative output regulation with exponential convergence is ensured for the resulting multi-agent system. The results of the paper are applied to the cooperative output regulation of a heterogeneous network of four parabolic agents in the presence of local disturbances.

本文关注的是具有抛物线偏微分方程描述的具有不同动力学的代理商网络的协作输出调节问题，该抛物型偏微分方程受空间和时变参数的影响。首先，设计了一个网络控制器，以实现相同有限维参考模型的输出同步，该同步模型将同步所需的全局参考模型的状态传递给抛物线代理。后者可能会受到局部干扰，作用于域内，在所有边界上以及在要控制的反并置输出上。通过为抛物线代理设计局部输出反馈调节器，可以解决协作输出调节问题。这就要求求解时变调节器方程，并设计具有空间和时变系数的抛物线系统的扰动观测器。为此，提供了一种系统的反推方法，结果表明，对于所得的多智能体系统，确保了具有指数收敛性的协同输出调节。本文的结果被应用于存在局部扰动的四个抛物线代理异质网络的协同输出调节。