论文标题
通过沉浸于离散时间非线性系统的浸入不变集的计算
Computation of invariant sets via immersion for discrete-time nonlinear systems
论文作者
论文摘要
在本文中，我们提出了一种通过将非线性动力学提升为更高维线性模型来计算离散时间非线性系统不变的方法。特别是，我们专注于某些给定约束集中包含的\ emph {Maximal允许不变集}。对于特殊类型的非线性系统，可以精确地浸入具有状态转换的较高维度线性系统中，可以使用较高的维度线性表示来表征原始非线性系统的不变集。对于一般的非线性系统，\ emph {近似沉浸式}在某些公差内定义在局部区域中，并通过利用不变式集合的固定点迭代技术来计算线性近似值。考虑到线性近似与原始系统之间的不匹配，我们通过拧紧过程提供了\ emph {Maximal Advension formant formiant Set}的不变内近似。
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible invariant set} contained in some given constraint set. For special types of nonlinear systems, which can be exactly immersed into higher dimensional linear systems with state transformations, invariant sets of the original nonlinear system can be characterized using the higher dimensional linear representation. For general nonlinear systems without the immersibility property, \emph{approximate immersions} are defined in a local region within some tolerance and linear approximations are computed by leveraging the fixed-point iteration technique for invariant sets. Given the bound on the mismatch between the linear approximation and the original system, we provide an invariant inner approximation of the \emph{maximal admissible invariant set} by a tightening procedure.
