具有边界和内部扰动的偏微分方程网络系统自适应输出反馈同步控制器

This work considers synchronizing controller design for a class of networked distributed parameter systems with structured time-varying perturbations and general disturbances. These systems are assumed to have unknown structured time-varying perturbations and unknown disturbances which are not constants any more. The task of the controllers is multiple. One is to asymptotically compensate both structured perturbation and disturbance effects. Additionally, to follow a virtual leader by ensuring the asymptotic convergence of each of the networked states to the virtual leader’s state. Finally, to synchronize in the sense of the convergence of the pairwise state errors. An observer-based feed-back controller is proposed to address all the tasks mentioned above and provides many new elements for control of networked spatially distributed systems. Infinite-dimensional observers are built to estimate the total disturbance which is made of structured time-varying perturbations and unknown disturbances include a consensus term in their adaptive laws which provide the first coupling of the networked systems and aims at providing a weak version of persistence of excitation. The consensus protocol included in the synchronization component of the controller addresses the communication burden by transmitting output signals to its communicating systems instead of entire states and further, adapts the synchronization weights in proportion to the pairwise state disagreement. An abstract theoretical framework is established which handles a wide class of infinite dimensional systems including PDEs with the observer systems, and the well-posedness and stability analysis is given in the approximate state spaces. By using Lyapunov stability arguments for infinite dimensional systems, the convergence of the networked states to the virtual leader’s state is established. The well-posedness of the networked closed-loop system is shown by using established results on a semigroup approach.

本项目考虑一类具有边界和内部结构扰动的网络化波动系统输出反馈同步控制。假设这些系统具有相同的未知时变的结构扰动和未知时变干扰。控制器的目标有三个：第一，对结构扰动和干扰效应进行自适应补偿。 第二，通过确保每个网络状态渐近跟踪虚拟主系统的状态。第三，使得网络两两系统之间的状态误差在同步的意义上收敛到0。本项目拟采用自抗抗控制方法设计同步控制器。首先根据输入、输出设计扰动估计器，然后利用扰动的估计值设计控制器来抵消总扰动，然后根据系统信息交换方式设计同步控制自适应律。利用算子半群理论证明闭环系统的适定性和稳定性。我们考虑的系统在边界处的扰动是时变的信号，外部扰动也是时变的信号，更具有一般性和广泛性；所用的估计结构扰动和外部扰动的方法是构造观测器，而且我们构造的是无穷维的观测器，可以避免高增益。

多智能体系统一致性控制是目前控制领域的一个研究热点，涌现出了大量出色成果。但目前大多数工作主要集中在常微分方程描述的多智能体系统，由偏微分方程描述的多智能体系统并没有引起重视。由于物理世界的许多现象是由偏微分方程描述的，如雷达、噪音的控制是由波动方程所描述的系统的控制，工业中温度控制是热传导方程描述的系统的控制。因此，分布参数多智能体系统不仅是多智能体系统研究体系的完善，同时更深刻的揭示了智能体动态行为与时间和空间相关的内在属性。所以，分布参数多智能体的一致性控制研究具有强烈的实际背景，如不确定性时变扰动下影响下的工业加热炉的温度一致性控制问题是分布参数多智能体系统中的一个重要问题。我们基于自抗扰控制技术(ADRC)，设计了具有补偿时变扰动功能的同步控制器，克服了非线性时变扰动对系统造成的不确定性影响，提高了系统的鲁棒性。仅利用每一个智能体的边界输出信息，建立了原系统的无穷维扩张状态观测系统，得到了扰动的实时估计值。利用多智能体一致性控制器设计同步与反馈补偿控制器，实现了各个子系统之间的状态同步。 此外，基于边界脉冲宽度调制(pulse width modulation，PWM)的控制技术，我们设计了基于边界输出采样信息的分段连续控制器，解决了边界脉冲宽度调制控制下的分布参数多智能体系统状态一致性问题。

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