A Framework Leveraging Asymmetry for Synchronization Stability in Networks of Coupled Dynamical Systems

许多自然和工程系统的功能依赖于耦合动力实体网络的稳定同步。一个突出的例子是电网网络，它依赖于发电机之间的同步运行。在这类系统的数学建模中，网络通常由定义节点的动态实体和定义节点之间相互作用的网络结构来表示。由于当代网络科学研究强调交互在引发涌现行为中的作用，因此现有研究主要集中在特定节点的网络结构优化上。然而，最近的研究表明，在许多情况下，优化节点参数是更可取的，这是一个问题，目前还没有足够的方法。该项目将开发和应用数学和计算方法，通过优化节点参数来提高与美国电网网络相关的同步稳定性。计划中的研究的成功完成预计将导致设计和操作原则，可以提高电网的稳定性。该项目还将为一名研究生和几名本科生提供跨学科的研究培训。该项目建立在最近的观察基础上，即显式对称破缺通常可以用于稳定网络系统中的同步状态。实现这一想法需要解决一个高维非凸优化问题，不能令人满意地解决现有的线性方法。该项目将开发和应用一种严格的非线性方法，以解决电网网络中的这类优化问题。该项目由四个部分组成：1）非线性二阶理论的发展，2）迭代数值算法的发展，实现理论，3）所产生的方法在美国电网中的应用，以及4）方法的应用研究条件下，显式对称破缺可以有利于稳定。预期的结果将带来稳定所需同步状态的新机会，并加深对有助于稳定的因素的理解。该项目是跨学科的，将为一名博士提供研究培训。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The function of numerous natural and engineered systems depends on the stable synchronization of networks of coupled dynamical entities. An outstanding case is that of power-grid networks, which rely on synchronization among power generators to operate. In the mathematical modeling of such systems, the networks are usually represented by the dynamical entities that define the nodes and the network structure that defines the interactions among nodes. Because contemporary research in network science emphasizes the role of interactions in giving rise to emergent behavior, existing studies have focused mainly on the optimization of the network structure for given nodes. Recent research has shown, however, that in many situations it is more desirable to optimize the node parameters, and this is a problem for which adequate methods do not currently exist. This project will develop and apply mathematical and computational methods to improve synchronization stability of relevance to the U.S. power-grid network by optimizing node parameters. Successful completion of the planned research is expected to lead to design and operation principles that can improve power-grid stability. The project will also provide interdisciplinary research training to one graduate student and several undergraduate students.The project builds on the recent observation that explicit symmetry breaking can often be used to stabilize synchronization states in network systems. Implementation of this idea requires solving a high-dimensional non-convex optimization problem that cannot be satisfactorily addressed by existing linear methods. The project will develop and apply a rigorous nonlinear method tailored to address this class of optimization problems in power-grid networks. The project consists of four parts: 1) the development of a nonlinear, second-order theory, 2) the development of an iterative numerical algorithm implementing the theory, 3) the application of the resulting methods to the U.S. power-grid network, and 4) the application of the methods to study conditions under which explicit symmetry breaking can benefit stability. The expected outcomes will lead to new opportunities for the stabilization of desired synchronous states and an improved understanding of the factors that contribute to stability. The project is interdisciplinary and will provide research training to one Ph.D. student and three summer undergraduate students, including students underrepresented in STEM, thereby advancing workforce development while promoting inclusion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.