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

本研究提出了一种估计大尺度非线性动力系统稳定区域的创新方法。所提方法的意义在于：(1)计算效率高；(2)在估计稳定区域时显著降低保守性；(3)适应性强（该方法非常通用，既可以单独使用，也可以与现有方法相结合，作为所提方法的输入）；(4)理论基础良好。目前，在估计大型非线性动力系统的稳定区域时，还没有一种计算上实用而又不产生不良保守结果的方法。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研究领域都是非常重要的。提出的研究就是为了满足这一迫切需要。此外，拟议的方法在方法发展领域和新应用领域开辟了新的研究领域。

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.