Fundamental limitations and complex dynamics in nonlinear network systems with uncertainty

本文的目的是发现和理解不确定性非线性网络系统的稳定性和估计性能的基本限制。具有不确定性的网络系统，如电网、互联网、基因调控网络、通信网络等，在科学和工程领域中普遍存在。不确定性的各种来源包括系统参数的不确定性、互连、信道延迟和丢失以及外部噪声。尽管它们无处不在，但人们对构建强大的网络系统的理解很少，并且缺乏系统的分析和设计工具。由非线性元素组成的网络系统的情况更加复杂，因为可能以复杂的非平衡动力学形式出现自我涌现行为。在这个建议中提出的研究将帮助我们了解在设计这样的网络系统的不确定性的基本限制。智力优点：在这个建议中开发的方法和工具的分析非线性网络系统的不确定性的启发随机动力系统的遍历理论。这一建议的变革思想是在扩展和发展的方法和工具，从遍历理论的随机动力系统的随机控制动力系统的目的是了解的基本性能限制的估计和控制的非线性网络控制系统的不确定性。扩展的形式主义导致的基本性能限制的不确定性非线性镇定的新结果。新的结果的主要亮点是，它指出了重要的角色所发挥的全球非平衡动力学的非线性系统在获得性能限制稳定。这个新的结果的全局性质，使他们从根本上不同于现有的性能限制的非线性稳定没有不确定性的结果，其中的限制表示在线性化的局部特征值。提出的研究基本性能的限制，在非线性估计与不确定性的动机是从应用问题的兴趣，建立一个强大的监视网络有限的传感器资源。联合技术公司对这个问题有应用兴趣，PI正在与联合技术研究中心（UTRC）合作解决这个问题。此外，发展遍历理论为基础的形式主义随机控制动力系统也将被用来解释出现的复杂动态，由于链路故障和不确定性的互连，在非线性网络控制system.Broader影响：出现的复杂动态，由于不确定性的结果将有助于预测网络系统的不稳定性和故障。与UTRC的研究合作，将为研究生提供机会，研究行业感兴趣的问题，并花时间在工业上。这种合作还将导致学术界和工业界之间的专门知识交流，反之亦然。该项目的跨学科性质将提供充足的机会，培养研究生在跨多个学科的前沿研究。

The objective of this proposal is to discover and understand the fundamental limitations on the stability and estimation performance of nonlinear network system with uncertainty. Network systems with uncertainty, such as the power grid, Internet, gene regulatory networks, and communication networks are ubiquitous in science and engineering. The various sources of uncertainty include uncertainty in system parameters, interconnection, channel delays and drop-outs, and external noise. In spite of their ubiquitous presence, there is very little understanding and a lack of systematic analysis and design tools for building robust networks systems. The situation of network systems consisting of nonlinear elements is further complicated because of the possibility of self-emergent behavior in the form of complex non-equilibrium dynamics. The proposed research in this proposal will help us understand the fundamental limitations in the design of such network systems with uncertainty.Intellectual Merit: The methods and tools to be developed in this proposal for the analysis of nonlinear network systems with uncertainty are inspired from the ergodic theory of random dynamical systems. The transformative idea of this proposal is in the extension and development of methods and tools from ergodic theory of random dynamical system to random control dynamical system for the purpose of understanding the fundamental performance limitations in the estimation and control of nonlinear network control systems with uncertainty. The extended formalism has lead to the new results on the fundamental performance limitations on nonlinear stabilization with uncertainty. The main highlight of the new results is that it point to the important role-played by the global nonequilibrium dynamics of nonlinear systems in obtaining performance limitations on stabilization. The global nature of this new result make them fundamentally different than the existing performance limitation results on nonlinear stabilization without uncertainty, where the limitations are expressed in terms of the local eigenvalues of the linearization. The proposed research on fundamental performance limitations in nonlinear estimation with uncertainty is motivated from the applied problem of interest of building a robust surveillance network with limited sensor resources. This problem is of applied interest to United Technologies Company and the PI is collaborating with United Technologies Research Center (UTRC) on this problem. Furthermore the developed ergodic theory-based formalism for random control dynamical systems will also be used to explain emergence of complex dynamics that arise due to link failures and uncertainty in interconnection, in the nonlinear network control system.Broader Impact: The results on the emergence of complex dynamics due to uncertainty will help predict the instabilities and failures of the network systems. The research collaboration with UTRC, will provide opportunity to graduate students to work on research problems of industry interest and spend time at industry. This collaboration will also lead to exchange of know-how between academia and industry and vice versa. The interdisciplinary nature of this project will provide ample opportunities to train graduate students in leading edge research that cuts across multiple disciplines.