报告题目：Low-rank balanced truncation via Laguerre functions

报告摘要：Many accurate modeling of physical phenomena often leads to large-scale dynamical systems that require long simulation time and large data storage and are unsuitable for control design. As a result, there is a growing interest in developing model order reduction (MOR) methods. The reduced-order models (ROMs) obtained by MOR can be efficiently used as surrogates for the original model and facilitate both the controller design and the computationally efficient analysis. In system and control theory, balanced truncation (BT) is the most commonly used classical MOR technique. In this talk, we will first introduce a BT approach based on low-rank Gramian approximation for linear systems. The goal of the approach is to construct the low-rank factors of the controllability and observability Gramians directly from the Laguerre functions expansion coefficient vectors of the matrix exponential functions by a recurrence formula. Then, use them to generate approximate balanced system for the large-scale system and obtain the ROMs by truncating the states corresponding to the small approximate Hanke singular values (HSVs). Secondly, we extend the above approach to bilinear systems and discrete-time systems successfully and a series of corresponding low-rank BT algorithms are derived.

报告人简介：肖志华，副教授，硕士生导师，长江大学数学学院数据科学系主任，德国纽伦堡大学访问学者。2015年获西安交通大学数学专业博士学位。主要研究方向为大规模复杂动态系统建模与降阶及其应用。主持国家自然科学基金项目2项、科技部外国专家项目1项、湖北省教育厅中青年人才项目1项，在国内外学术期刊上发表学术论文30余篇。

报告时间：2024年05月30日10:20-11:20

报告地点：同析4号楼 322会议室