CAREER: Novel Representations for Distributed Control of String Networks in Vehicle Platooning and Supply Chain Management

一类振荡行为，通常被称为蝴蝶效应或牛鞭效应，对于电力网络、供应链或运输网络等大规模动力系统网络来说是相当习惯的。它们本质上描述为在网络的一个区域发生的功能参数的微小扰动（或波动），在通过网络的动态传播时开始放大，并最终导致与网络其他部分的运行参数的极大偏差。这种不希望出现的现象在重要的实际应用中很常见，而且很难避免。提出了一种由PI引入的动态网络的新颖数学描述，它能够同时捕获给定网络的动态和拓扑。对于一串动态智能体（车辆队列）的初步结果表明，结合经典控制理论的概念和方法，这种新的数学描述将为分布式控制器设计的实际方法的发展提供研究。对于具有线性和时不变动态的网络，控制器的分布式特性被转换为控制器左素数因子上的稀疏性约束，与施加在闭环映射上的稀疏性约束串联使用。在描述网络特定节点的成本时，闭环映射上的约束保证了分布式最优控制器设计问题的可跟踪性，并表征了干扰在闭环中传播的方式，从而消除了牛鞭效应。目标是研究反馈回路内部稳定性概念所需的适应性，这在当前的分布式控制器实现范例中是必要的。

A certain class of oscillatory behaviors, popularly known as the butterfly effect or the bullwhip effect are quite habitual to large scale networks of dynamical systems, such as electrical networks, supply chains or transportation networks. They essentially describe as tiny perturbations (or fluctuations) in the functional parameters occurring in one area of the network, start to amplify while propagating through the dynamics of the network and ultimately result in extremely large deviations from the operational parameters in other parts of the network. This undesired phenomenon is very common and difficult to avert in important practical applications. The proposal brings forth a novel mathematical description of dynamical networks introduced by the PI, which is capable of capturing simultaneously both the dynamics and the topology of a given network. Preliminary results for the case of a string of dynamical agents (vehicles platooning) showed that coupled with concepts and methods from classical control theory, this new mathematical description will be investigated for the development of practical methods for the design of distributed controllers.For the case of networks with linear and time invariant dynamics, the distributed nature of the controller is cast as sparsity constraints on the controller left coprime factors, to be used in tandem with sparsity constraints imposed on the closed-loop maps. While delineating costs to specific nodes of the network, the constraints on the closed-loop map guarantee the tractability of the distributed, optimal controller design problem and characterize the manner in which disturbances propagate through the closed loop, thus eliminating the bullwhip effect. The goal is to investigate the needed adaptation of the concept of internal stability of the feedback loop, which becomes necessary in the current paradigm of the distributed implementation of controllers.