CAREER: Stability analysis and control of uncertain network controlled system in nonequilibrium

对于偏离平衡运行的不确定网络控制动态系统，本研究将发现用于a)预测具有多个不确定源的网络系统的不稳定性；b)识别导致网络中非平衡动态出现的反馈机制和关键参数；c)一类网络控制动态系统的控制器设计的分析方法和计算工具。这一建议的理论发现是为了将其应用于电网、稳定裕度的计算和电力系统的在线暂态稳定分析。智力上的优点：所提出的研究是对动态系统遍历理论和控制方法的统一和发展，目的是将其应用于具有不确定性的网络控制动态系统。我们提出的方法的显著特点是，它以统一的方式处理了特定于网络系统的不确定性放大的几个方面。也就是说，它允许我们处理通信链路的不确定性、系统交互中的不确定性以及网络系统演化中的不确定性。这一统一的框架使得PI在分析和控制网络上的不确定非线性系统方面做出了两项基本贡献。第一个贡献是利用基于遍历理论的框架，为非线性系统中复杂非平衡动力学的稳定性验证和控制设计提供了基于线性规划的分析和计算解。第二个贡献来自于对输入和输出通道具有不确定性的非线性系统的镇定和观测的基本极限结果的推导。PI建议进一步扩展这些方法，以发现用于分析和控制网络控制动态系统的分析方法和计算工具，特别关注于解决网络系统中的两个主要挑战，即网络系统中的不确定性和自涌现的非平衡动力学。广泛影响：建议中开发的理论和计算工具已应用于网络系统的新兴领域，包括生物网络和社会网络。我们在识别网络系统中复杂非平衡动力学出现的反馈机制方面的结果可以应用于生物网络，以帮助理解遗传修饰的后果，并指导改变这种行为的实验设计。对于疾病传播等社会网络，所提出的基于不确定性的建模框架和理论研究可以为流行病的预防或传播提供条件。该项目的跨学科性质将为培养跨多学科前沿研究的研究生提供充足的机会。这些跨学科的组成部分将被整合到更大的教育努力中，为工科学生提供坚实的基础，并在复杂系统以及控制和动力学方面进行培训。

For uncertain network controlled dynamical systems operating away from equilibrium, the proposed research will discover analytical methods and computational tools for the a) prediction of instabilities in network systems with multiple sources of uncertainties; b) identification of feedback mechanisms and critical parameters responsible for the emergence of nonequilibrium dynamics in networks; c) design of controller for a class of network control dynamical systems. The theoretical discovery of this proposal is motivated with regard to its application to the electric power grid, for the computation of stability margin and for online transient stability analysis in power systems.Intellectual Merit: The proposed research is in the unification and development of methods and tools from the ergodic theory of dynamical systems and control approaches for the purpose of its application to network controlled dynamical systems with uncertainty. The distinctive feature of our proposed approach is that it treats several aspects of uncertainty amplification specific to networked systems in a unified way. Namely, it allows us to handle the uncertainty of the communication links, the uncertainty in the system interactions, and the uncertainty in the networked system evolution. This unified framework has allowed the PI to make two fundamental contributions for the analysis and control of uncertain nonlinear systems over networks. The first contribution is in the use of ergodic theory-based framework to provide linear programming-based analytical and computational solution for stability verification and control design of complex nonequilibrium dynamics in nonlinear system. The second contribution arises in the derivation of fundamental limitation results for the stabilization and observation of nonlinear systems with uncertainty at the input and output channels. The PI propose to further extend these methods to discover analytical methods and computational tools for the analysis and control of network controlled dynamical systems with particular focus on addressing two main challenges, namely uncertainty and self-emergent nonequilibrium dynamics in the network systems.Broader Impact: The theoretical and computational tools developed in the proposal have applications in the emerging areas of network systems, including biological and social networks. Our results on identification of feedback mechanisms for the emergence of complex nonequilibrium dynamics in network systems can be applied to biological networks to help understand the consequence of genetic modification, and for guiding experiments design for modifying such behavior. For social networks such as disease spread, the proposed uncertainty-based modeling framework and theoretical research can be used to provide conditions for the prevention or spread of an epidemic. The interdisciplinary nature of this project will provide ample opportunities to train graduate students in leading-edge research that cuts across multiple disciplines. These interdisciplinary components will be integrated into a larger educational effort to offer engineering students a solid foundation and training in complex systems, as well as in control and dynamics.