Mini-workshop: Analysis, Numerics and Control

Date: Mon. March 27, 2023:
Event: FAU DCN-AvH Mini-workshop: Analysis, Numerics and Control
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Title: Null Controllability for Population Dynamics with age, size Structuring and Diffusion
Speaker: Prof. Dr. Yacouba Simpore
Affiliation: Visiting Scientist at FAU DCN-AvH from University of Fada N’Gourma


Abstract. It has been recognized that age structure alone is not adequate to explain the population dynamics of some species. The size of individuals could also be used to distinguish cohorts as carcinogenic cells. In principle there are many ways to differentiate individuals’ addition to age, such as body size and dietary requirements or some other physiological variables and behavioral parameters. In this talk, we discuss the null controllability of a class of infinite dimensional linear system describing population models structured by age, size, and spatial position. We establish the null controllability by using a technique that avoids the explicit use of parabolic Carleman estimates. Our argument relies on a method that combines final-state observability estimates with the use of the characteristic method.

Title: Low-rank balanced truncation for linear and bilinear systems via Laguerre polynomials
Speaker: Prof. Dr. Zhihua Xiao
Affiliation: Visiting Scientist from Yangtze University, China


Abstract. 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 aim is to generate reduced-order models (ROMs) that can accurately represent the behavior of the original systems under a variety of conditions. The ROMs 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 successfully and a series of corresponding low-rank BT algorithms for bilinear systems are derived.
This is based on joint work with Prof. Yao-Lin Jiang and Dr. Zhen-Zhong Qi.

Title: Model order reduction for linear systems via low-rank cross Gramian
Speaker: Qiuyan Song
Affiliation: Visiting PhD Student from Shanghai University


Abstract. Model order reduction (MOR) aims to find a fairly accurate lower order model which preserves the essential properties of the given large-scale system, such as the stability and input-output behaviors. It is a robust tool in simulation, analysis and optimal control. Due to cross Gramian contains the information on controllability and observability of a system at the same time, MOR based on such Gramian has received a lot of attention. In this talk, we will introduce an MOR method for square and non-square linear systems based on the low-rank decomposition of the cross Gramian. It combines ideas from low-rank square root method (LRSRM) and Legendre orthogonal polynomials. In contrast to traditional balanced truncation (BT) related approaches which require to solve a Sylvester equation to compute the full cross Gramian, the proposed method needs to solve sparse linear equations and only one SVD for a low-dimensional matrix is implemented, which makes it more flexible and computationally efficient. Furthermore, in combination with the dominant subspace projection method, the reduction procedure is modified to alleviate the shortcoming, which may unexpectedly lead to unstable ROMs even though the original system is stable.

This is based on joint work with Prof. Xin Du in Shanghai University.


On-site / Online

Room Übung 4. 1st. floor. Department Mathematik.
Friedrich-Alexander-Universität Erlangen-Nürnberg.
Cauerstraße 11, 91058 Erlangen.
GPS-Koord. Raum: 49.573639N, 11.030503E

Zoom meeting link
Meeting ID: 614 4658 1599 | PIN code: 914397

This event on LinkedIn
Previous FAU DCN-AvH Workshops:

Mini-workshop: “Analysis, Numerics and Control” by Djida, Wang, Álvarez (November 14th, 2022)
Mini-workshop: “Analysis, Numerics and Control” by Parada, Crin-Barat (November 11th, 2022)
Mini-workshop: “Recent Advances in Analysis and Control” by Aceves, Paoli and Sarac (July 1st, 2022)
Mini-workshop: “Recent Advances in Analysis and Control” by Simpore, Crin-Barat, Biccari (June 20th, 2022)
Mini-Workshop “Calculus of Variations and Functional Inequalities” by König, Glaudo (May 25th, 2022)
Mini-workshop: “Model Reduction and Control” by Peitz, Manzoni, Strazzullo (May 24th, 2022)
Seminar Series: Deep Learning in Control by Heiland (January 17th, 2022)
Mini-workshop: “Recent Advances in Analysis and Control” by Lazar, Zamorano, Lecaros (January 14th, 2022)
Mini-workshop: “Recent Advances in Analysis and Control” by Ftouhi, Rodríguez, Song, Matabuena (October 1st, 2021)
Mini-workshop: “Recent Advances in Analysis and Control” (II) by Sônego, Minh Binh Tran (May 21th, 2021)
Mini-workshop: “Recent Advances in Analysis and Control” by Della Pietra, Wöhrer, Meinlschmidt (April 30th, 2021)