平方和规划吸引可达区域的时空分解
Spatio-Temporal Decomposition of Sum-of-Squares Programs for the Region of Attraction and Reachability
摘要：
本文提出了一种利用半定规划问题（SDP）求解受控多项式动力系统目标集（不一定是平衡点）吸引域的方法。我们的方法建立在以前的工作，并解决其主要问题，快速增长的内存需求，解决大规模的SDP。这项工作的主要思想是将原始的资源需求问题分解为多个较小的，相互关联的，更容易解决的问题。这是通过类似于基于偏微分方程的方法的时空分裂来实现的。我们表明，分裂过程保留了以前的工作的收敛性和外近似保证，同时在更短的时间内实现更高的精度和更小的内存占用。
英文摘要：
This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach builds on previous work and addresses its main issue, the fast-growing memory demands for solving large-scale SDPs. The main idea in this work is in dissecting the original resource-demanding problem into multiple smaller, interconnected, and easier to solve problems. This is achieved by spatio-temporal splitting akin to methods based on partial differential equations. We show that the splitting procedure retains the convergence and outer-approximation guarantees of the previous work, while achieving higher precision in less time and with smaller memory footprint.
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