2017 ACC Workshop on

Ensemble Control

 

Control of Inhomogeneous Ensembles (40 minutes)

Jr-Shin Li

Department of Electrical and Systems Engineering

Washington University in St. Louis

St. Louis, MO, USA


Abstract

In this talk, a survey of emerging techniques and research problems in the field of ensemble control will be presented. State-of-the-art results in analyzing controllability of ensemble systems and computational methods for computing optimal controls involving an ensemble system will be introduced. The applications of the developed theoretical and numerical approaches to practical control designs, including entrainment of nonlinear oscillators, synchronization of brain networks, and excitation of quantum ensembles, will also be illustrated and discussed.


Bio:

Jr-Shin Li received his BS and MS degrees from National Taiwan University, and his PhD degree in Applied Mathematics from Harvard University in 2006. He is currently an Associate Professor in Electrical and Systems Engineering with a joint appointment in the Division of Biology & Biomedical Sciences at Washington University in St. Louis. His research interests are in the areas of dynamics and control, computational mathematics, optimization, and complex networks. His current work involves the control of large-scale complex systems with applications ranging from quantum mechanics and neuroscience to chronobiology. He has been a recipient of the NSF Career Award in 2007 and the AFOSR Young Investigator Award in 2009.

 

In this workshop, we will offer a survey of emerging techniques and research problems in the field of Ensemble Control. Emphasis will be placed on both recent theoretical developments and emerging applications at the interface between systems science and control engineering, physics, neuroscience, and biology. We will introduce state-of-the-art methods for theoretical investigation of fundamental properties of ensemble systems, including controllability and observability, and discuss computational methods for the synthesis of optimal ensemble controls. We will also describe the use of ensemble control theory for various applications including characterization of neurons in diseased networks (e.g., Parkinson’s disease, epilepsy), entrainment of a population of nonlinear oscillators, and transport of particles over networks. Finally, various fundamental and practical problems in ensemble control will be articulated and discussed.

 

Presentations:

Ensemble Observability of Dynamical Systems (40 minutes)

Shen Zeng

Institute for Systems Theory and Automatic Control

University of Stuttgart

Stuttgart, Germany


Frank Allgöwer

Institute for Systems Theory and Automatic Control

University of Stuttgart

Stuttgart, Germany


Abstract

In solving applied problems related to population systems, such as in cell biology, a frequently met task is to first extract information about the parameter distribution within a population of systems from distributional measurement / population snapshot data. In this talk, we will focus on the theoretical core of this practical estimation problem, the ensemble observability problem, which consists of reconstructing a density of initial states from the evolution of the density of outputs under a finite-dimensional dynamical system. A fundamental result in the study of the ensemble observability problem is an inherent connection to mathematical tomography problems. We aim to give a broad overview of the ensemble observability problem for both linear and nonlinear systems.


Bio:

Shen Zeng studied Engineering Cybernetics, Mechatronics, and Mathematics at the University of Stuttgart, where he also received a Ph.D. degree in 2016. He is currently a postdoctoral researcher at the Institute for Systems Theory and Automatic Control, University of Stuttgart. His research interests are in systems and control theory with a focus on analytic, algebraic, and geometric methods.


Frank Allgöwer studied Engineering Cybernetics and Applied Mathematics in Stuttgart and at University of California, Los Angeles (UCLA), respectively, and received the Ph.D. degree in chemical engineering from the University of Stuttgart, Stuttgart, Germany. He is the Director of the Institute for Systems Theory and Automatic Control, the University of Stuttgart. Since 2012, he has been serving as the Vice President of the German Research Foundation DFG, Bonn, Germany. His research interests include cooperative control, predictive control, and nonlinear control with application to a wide range of fields including systems biology. At present, Frank is President Elect of the International Federation of Automatic Control IFAC.

Optimal Control of an Epileptic Neural Population Model (40 minutes)

Justin Ruths

Mechanical Engineering

University of Texas as Dallas


Abstract

Neural population models describe the macroscopic neural activity that can be clinically recorded by an electroencephalogram (EEG). Such models are relevant for the investigation of many pathological neurological phenomena including epilepsy and Parkinson's disease because the models operate on the same scale as the recorded data. Although several models exist in the neuroscience literature, none have leveraged the systematic approach of optimal control theory to design stimuli to treat such neurological conditions. In this talk, I will present the model, a formulation of the seizure abatement goal expressed as an optimal ensemble control problem, as well as a computational method to solve this problem using an adapted pseudospectral method. I will show several results including a realistic, noise-driven simulation where the control is applied as needed in a moving window.


Bio:

Justin Ruths received a B.S. in Physics from Rice University, M.S. degrees in Mechanical and Electrical Engineering from Columbia University and Washington University in Saint Louis, respectively, and a Ph.D. in Systems Science and Applied Mathematics from Washington University in Saint Louis. In 2011, Dr. Ruths joined Engineering Systems and Design as a founding faculty member of Singapore University of Technology and Design where he served as an assistant professor for five years. As of August 2016 he is an assistant professor with appointments in Mechanical Engineering and Systems Engineering at University of Texas at Dallas. His research includes studying the fundamental properties of controlling networks, bilinear systems theory, attack detection methods for cyber-physical systems, and solving computational optimal control problems focused on neuroscience and quantum control applications.

Ensemble Controllability of Parametric Systems (40 minutes)

Michael Schoenlein

Institute for Mathematics

University of Wuerzburg

Wuerzburg, Germany


Abstract

In this talk we consider classes of parametric ensembles of systems which are defined by a parameter dependent family of linear control systems. Using well-known characterizations of approximate controllability of systems in a Banach space, we present a unified approach to uniform ensemble control of parameter-varying linear systems. Both time-invariant and time-varying linear systems are treated, leading to new necessary and sufficient conditions for ensemble controllability. We also present an approach for the construction of the control inputs steering the ensemble towards the desired family of terminal states.


Bio:

Michael Schoenlein studied Mathematics at the University of Wuerzburg, where he also received a PhD degree. He is currently a postdoctoral researcher at the Institute for Mathematics, University of Wuerzburg. His research interests are in mathematical control theory and stability theory of dynamical systems.

Parallel Connections and Infinite Bilinear Ensembles on Lie Groups (40 minutes)

Gunther Dirr

Institute for Mathematics

University of Wuerzburg

Wuerzburg, Germany


Abstract

We present necessary and sufficient conditions for accessibility of parallel connected bilinear systems. From this, we derive controllability criteria for finite ensembles on semi-simple Lie groups. Then, we generalize the previous concepts in a second step to infinite bilinear systems regarded as bilinear systems on infinite dimensional Banach Lie groups. We present first results for driftless systems and highlight major problems occurring in systems with drift.


Bio:

Gunther Dirr was born in 1968 and studied Mathematics and Physics at the University of Ẅürzburg, Germany. He received his Diploma and Ph.D. in Mathematics in 1995 and 2001, respectively. He has held post-doctoral positions at the University of Würzburg and the Technical University of Munich. Currently, he is an Assistant Professor at the Chair of Mathematics II, Dynamical Systems and Control Theory, at the Institute of Mathematics, University of Würzburg. His major research interests are nonlinear geometric control theory and optimal control including bilinear control, invariant systems on Lie groups and homogeneous spaces as well as their applications to quantum control.

Modeling and Control of Collective Dynamics (40 minutes)

Tryphon Georgiou

Department of Mechanical and Aerospace Engineering

University of California, Irvine


Yongxin Chen

Memorial Sloan Kettering Cancer Center, New York


Michele Pavon

Department of Mathematics, University of Padova, Italy


Abstract

We will discuss the impact of new theoretical advances, by the authors and others, on the classical problems of Monge-Kantorovich optimal mass transport and Schrodinger bridges, to modeling and simultaneous control of collections of dynamical systems. In particular, the newly developed theory and insights provides a geometric framework that allows quantifying distances between distributions and casts problems of steering and control of ensembles as convex optimization problems.


Bio:

Tryphon T. Georgiou received the Diploma in Mechanical and Electrical Engineering from the National Technical University of Athens, Greece, in 1979 and the Ph.D. degree from the University of Florida, Gainesville, in 1983. He is a faculty in the Department of Mechanical and Aerospace Engineering at the University of California, Irvine and the Chancellor’s Professor. He is a recipient of the George S. Axelby Outstanding Paper award of the IEEE Control Systems Society for the years 1992, 1999, and 2003, a Fellow of the Institute of Electrical and Electronic Engineers (IEEE), and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).


Yongxin Chen received his BSc in Mechanical Engineering from Shanghai Jiao Tong university, China, in 2011. He obtained his Ph.D. in Mechanical Engineering from University of Minnesota in 2016 under the supervision of Tryphon Georgiou, with a Ph.D. minor in Mathematics. He is now a postdoc fellow in the Department of Medical Physics in Memorial Sloan Kettering cancer center. He is interested in the application of mathematics in engineering, physics and biology. His current research focuses on linear dynamical systems, stochastic processes, optimal mass transport theory and system biology.