论文标题
对单方面Lipschitz和二次内部结合的非线性动态系统的新见解
New Insights on One-Sided Lipschitz and Quadratically Inner-Bounded Nonlinear Dynamic Systems
论文作者
论文摘要
非线性动态系统可以根据建模的非线性分类为各个类。这些课程包括Lipschitz，有限的Jacobian，单方面Lipschitz（OSL）和四跨内部结合（QIB）。这些类实质上是屈服界定常数，表征了非线性。然后，这用于通过Riccati方程或矩阵不等式设计观察者和控制器。尽管在文献中研究了Lipschitz和有限的Jacobian非线性的界定常数的分析表达式，但在计算或分析上未彻底分析OSL和QIB类。简而言之，本文开发了OSL和QIB边界常数的分析表达式。这些表达式被构成受约束的最大化问题，可以通过各种优化算法解决。本文还提出了一种新颖的见解，尤其是对QIB函数集：QIB的任何函数也是Lipschitz的连续。
Nonlinear dynamic systems can be classified into various classes depending on the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian, one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes essentially yield bounding constants characterizing the nonlinearity. This is then used to design observers and controllers through Riccati equations or matrix inequalities. While analytical expressions for bounding constants of Lipschitz and bounded Jacobian nonlinearity are studied in the literature, OSL and QIB classes are not thoroughly analyzed---computationally or analytically. In short, this paper develops analytical expressions of OSL and QIB bounding constants. These expressions are posed as constrained maximization problems, which can be solved via various optimization algorithms. This paper also presents a novel insight particularly on QIB function set: any function that is QIB turns out to be also Lipschitz continuous.
