论文标题
使用半决赛编程将外部近似值融合到全球吸引子
Converging outer approximations to global attractors using semidefinite programming
论文作者
论文摘要
本文开发了一种方法，用于获得连续和离散时间非线性动力学系统的全局吸引子的保证外近似值。该方法是基于半标准编程问题的层次结构，该问题的规模增加了大小，并保证收敛到全球吸引子。采用的方法遵循建立的推理线，我们首先通过无限的尺寸线性编程问题（LP）在Borel措施的空间中对全球吸引子进行表征。该LP的双重偶在连续功能的空间中，其可行解决方案为全球吸引子提供了保证的外部近似值。对于具有多项式动力学的系统，双LP的有限维平价拧紧的层次结构为全局吸引子提供了一系列外部近似值，并在体积差异的趋势趋势趋于零的情况下保证了收敛。该方法非常易于使用，并且纯粹基于凸优化。在线可用代码的数值示例演示了该方法。
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of increasing size with guaranteed convergence to the global attractor. The approach taken follows an established line of reasoning, where we first characterize the global attractor via an infinite dimensional linear programming problem (LP) in the space of Borel measures. The dual to this LP is in the space of continuous functions and its feasible solutions provide guaranteed outer approximations to the global attractor. For systems with polynomial dynamics, a hierarchy of finite-dimensional sum-of-squares tightenings of the dual LP provides a sequence of outer approximations to the global attractor with guaranteed convergence in the sense of volume discrepancy tending to zero. The method is very simple to use and based purely on convex optimization. Numerical examples with the code available online demonstrate the method.
