Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond
Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond
复制标题
DOI：
10.1109/tac.2021.3110895
复制
发表时间：
2020-04
影响因子：
6.8
通讯作者：
Sebastian A. Nugroho;A. Taha;V. Hoang
中科院分区：
文献类型：
--
作者：
Sebastian A. Nugroho;A. Taha;V. Hoang
在过去的三十年里，针对非线性动态系统（NDS）的状态反馈和观测器设计已经发展了许多。这些设计假设NDS非线性满足下列函数集分类之一：有界Jacobian、Lipschitz连续性、单侧Lipschitz、二次内有界性和二次有界性。这些函数集的特征是常数标量或矩阵包围NDS的非线性。这些常数取决于NDS的工作区域、拓扑和参数，并用于综合观测器/控制器增益。不幸的是，目前几乎完全没有计算这种边界常数的算法。在本文中，我们发展了计算这些常数的解析和计算方法。首先，对于每个函数集分类，我们通过全局最大化公式推导出这些边界常数的解析表达式。其次，利用基于分支定界框架的无导数区间全局最大化算法，数值求出边界常数。第三，我们展示了我们的方法在一些NDS（如高速公路交通网络和同步发电机模型）上计算相应参数的有效性。
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 depend on the NDS’ operating region, topology, and parameters and are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this article, we develop analytical and 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 the 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.