BECS: Collaborative Research: Characterization and Control of Emergent Behavior in Complex Systems

目前在复杂网络系统领域的知识状态缺乏能够准确预测的正式理论，因此有助于控制此类系统的行为。该项目的科学目标是建立一个理论基础，以理解，分析和控制在不确定环境中运行的复杂系统的紧急行为。为了验证理论思想，该项目特别考虑了复杂的群体机器人系统，旨在将所提出的分析框架应用于此类系统。中央的方法使用随机微分方程的数学框架，其中的群被视为一个耗散的哈密顿系统耦合的非线性相互作用的潜力。在这个框架内，不确定性（噪声）的影响进行处理数学上使用的离散和连续制剂从福克-普朗克方法获得。本研究的重点是发展的理论基础，复杂系统的建模和分析的基础上给定的控制输入和固有的系统不确定性。该框架有利于对复杂系统中的复杂交互、高维性、非线性和不确定性进行建模，以及对期望的紧急行为进行控制。这项研究的潜在未来应用包括电网和通信网络。此外，该项目具有更广泛的影响，包括促进教学、培训和学习;广泛传播以增进了解;以及代表性不足群体的参与。本科生和研究生通过课程和参与研究和外联活动得到指导和培训。广泛的传播是通过特别会议，研讨会和辅导会议，目标都是动态系统和控制以及数学界。通过暑期项目、夏令营和其他方案，如妇女在科学和工程以及新兴民族工程师，促进了来自代表性不足群体的本科生和学生的参与。

The current state of knowledge in the area of complex networked systems lacks formal theories that can accurately predict, and hence help control the behavior of such systems. The scientific objective of this project is to develop a theoretical basis to understand, analyze, and control emergent behavior in complex systems operating in uncertain environments. In order to validate the theoretical ideas, the project specifically considers complex swarm robotic systems and aims to apply the proposed analytical framework to such systems. The central approach uses the mathematical framework of stochastic differential equations wherein the swarm is treated as a dissipative Hamiltonian system coupled by nonlinear interacting potentials. In this framework, the influence of uncertainties (noise) is treated mathematically using both the discrete and continuum formulations to be obtained from a Fokker-Planck approach. The focus of this research is the development of a theoretical basis for modeling of complex systems and their analysis based upon given control inputs and inherent system uncertainty. This framework facilitates modeling the complex interactions, higher-dimensionality, nonlinearity, and uncertainty in complex systems as well as the control of desirable emergent behavior. Potential future applications of this research include power grids and communication networks. Furthermore, this project has broader impacts that include promoting teaching, training, and learning; broad dissemination to enhance understanding; and involvement of the underrepresented groups. Undergraduate and graduate students are mentored and trained via courses and involvement in research and outreach activities. Broad dissemination is achieved through special sessions, workshops, and tutorials at conferences that target both the dynamic systems and control as well as mathematics communities. Participation of undergraduates and students from underrepresented groups is facilitated via summer projects, summer camps, and other programs such as Women in Science and Engineering and Emerging Ethnic Engineers.