Collaborative Research: A Distributed Approximate Dynamic Programming Approach for Robust Adaptive Control of Multiscale Dynamical Systems

该项目将开发一种用于管理和控制复杂系统的新型通用多智能体系统，在该系统中，面对非线性和复杂性，各智能体以完全合作的方式共同工作，以最大限度地提高全局性能。作为验证新方法价值的试验台，他们将模拟以下挑战：(1)地震响应，代表着一类发生非常快、提前时间短、地理范围有限的灾害；(2)旱灾救灾，代表着预测和准备时间较长、地理范围较大的一类灾害。研究结果将被广泛传播，并将用于教育和推广项目，包括杜克大学的本科生研究体验(REU)网站和NSF资助的无线智能传感器网络IGERT，提供给暑期学校和国际合作伙伴。这里的关键挑战是开发一种完全分布式的新版本的自适应近似动态编程(ADP)，以解决多尺度动态系统的情况。这项工作建立在领导PI在分布式最优控制(DOC)方面的最新工作基础上，包括开发用于系统部分降维的最优限制算子，以及开发偏微分方程组(PDE)和随机微分方程组(SDE)领域的方法。

This project will develop a new type of general multiagent system for management and control of complex systems, in which the agents work together in a fully cooperative way to maximize global performance over time, in the face of nonlinearity and complexity. As a testbed to prove the value of the new approach, they will simulate the challenges of: (1) earthquake response, representing a class of disasters with very rapid occurrence, short lead times and restricted geographic extent; and (2) drought-induced famine relief, representing the class of disasters with longer forecast and lead times, and larger geographic extent. The results will be widely disseminated and will feed into programs for education and outreach, including a Research Experience for Undergraduates (REU) site at Duke and the NSF-funded IGERT on Wireless Intelligent Sensor Networks, feeding into summer schools and international partnerships.The key challenge here is to develop a new version of adaptive, approximate dynamic programming (ADP) which is fully distributed,to address the case of multiscale dynamical systems. The work builds on recent work of the lead PI on Distributed Optimal Control (DOC), and includes development of optimal restriction operators for dimensionality reduction in parts of the system, and exploitation of methods from the field of partial differential equations (PDE) and stochastic differential equations (SDE).