结构线性时不变多变量状态空间模型的识别
Identification of Structured LTI MIMO State-Space Models
AI总结：
本文提出一种基于差分凸规划的算法，通过将双变量优化转换为低秩约束优化问题，以高效求解结构状态空间模型的全局最优解。
摘要：
结构状态空间模型的识别长期以来备受关注，但仍未得到充分解决。主要挑战在于涉及的估计问题是一个非凸（或双变量）优化问题。本文致力于开发一种识别方法，旨在在计算负担较小的情况下找到全局最优解。开发的识别算法关键在于将双变量估计转换为秩约束优化问题，并进一步转换为差分凸规划（DCP）问题。DCP问题的初始条件通过求解其优化问题的凸部分获得，该部分恰好是一个核范数正则化优化问题。由于核范数正则化优化是低秩约束估计问题的最接近凸形式，因此获得的初始条件始终具有高质量，为DCP问题提供了良好的起点。然后通过顺序凸规划方法求解DCP问题。最后，数值示例展示了所开发的识别算法的有效性。
英文摘要：
The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
