Research Initiation: An Innovative Methodology for Estimating the Stability Regions of Large-Scale Nonlinear Dynamical Systems

这项研究提出了一种新的方法来估计大规模非线性动力系统的稳定区域。该方法的意义包括：(1)计算效率；(2)显著降低估计稳定区域的保守性的能力；(3)其适应性(该方法非常通用；它可以独立存在，也可以与现有方法相结合，以服务于该方法的输入)；(4)其良好的理论基础。目前，对于大规模非线性动力系统的稳定域估计，还没有一种计算上实用的方法，也没有得到令人满意的保守结果。这种实用方法的存在对于许多工程和科学应用以及许多新兴的研究领域都是非常重要的。拟议的研究就是为了满足这一迫切需求。此外，拟议的方法开辟了新的研究领域，无论是在方法发展领域还是在新的应用领域。

This research proposes to develop an innovative methodology for estimating the stability regions of large-scale nonlinear dynamical systems. The significance of the proposed methodology include: (1) its computational efficiency, (2) its ability to significantly reduce the conservativeness in estimating the stability regions, (3) its adaptability (this methodology is very general; it can stand by itself or it can be synthesized with existing methods in the way that they serve the input of the proposed methodology) and (4) its sound theoretical basis. At present, there does not exist any method that is computationally practical, yet does not yield undesirably conservative result in estimating the stability regions for large- scale nonlinear dynamical systems. The existence of such a practical method is very important for many engineering and scientific applications, as well as for many emerging research areas. The proposed research is to meet this pressing need. Also, the proposed methodology opens new areas for research, both in the area of methodology development and in the area of new applications.