微分代数方程的解作为线性时不变系统的输出：在线性二次控制问题中的应用
最优化与控制
2016-11-02 v6
摘要
本文综合了行为主义思想与几何控制理论，提出了一个统一的几何框架，将线性时不变微分代数方程 (DAE-LTI) 的所有解表示为经典线性时不变系统 (ODE-LTI) 的输出。文中描述了一种计算生成给定 DAE-LTI 解的 ODE-LTI 的算法。研究表明，表示同一 DAE-LTI 的两个不同 ODE-LTI 是反馈等价的。随后，利用该框架解决了具有矩形矩阵的 DAE-LTI 的线性二次 (LQ) 最优控制问题。
引用
@article{arxiv.1312.7547,
title = {Solutions of differential-algebraic equations as outputs of LTI systems: application to LQ control problem},
author = {Mihaly Petreczky and Sergiy Zhuk},
journal= {arXiv preprint arXiv:1312.7547},
year = {2016}
}
备注
The main difference with respect to the previous version is that the supplementary files were included which were missing from the previous version. Note that part of the material of this report appeared in arXiv:1309.1235. A version of this paper was submitted to Automatica, first in January 2014 and then in November 2014, and then in November 2015