论文标题
非线性动态系统参数化使用基于间隔的全局优化：计算Lipschitz常数及其他
Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond
论文作者
论文摘要
在过去的三十年中，已经开发了许多针对非线性动态系统（NDS）的国家反馈和观察者设计。这些设计假定NDS非线性满足以下功能集分类之一：有限的Jacobian，Lipschitz的连续性，单方面Lipschitz，二次内部结合性和二次界限。这些函数集的特征是恒定标量或矩阵界定NDS的非线性。这些常数（i）取决于NDS的操作区域，拓扑和参数，并且（II）用于合成观察者/控制器的收益。不幸的是，几乎没有算法来计算这种边界常数。在本文中，我们开发了分析方法，然后计算方法来计算此类常数。首先，对于每个函数设置分类，我们通过全局最大化制定得出这些边界常数的分析表达式。其次，我们利用基于分支和结合框架的基于无衍生的，基于间隔的全局最大化算法来获得数值获得边界常数。第三，我们展示了我们的方法的有效性，以计算某些NDS上的相应参数，例如高速公路交通网络和同步发电机模型。
Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by constant scalars or matrices bounding the NDS' nonlinearities. These constants (i) depend on the NDS' operating region, topology, and parameters, and (ii) are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this paper, we develop analytical then computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free, interval-based global maximization algorithm based on branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models.
