Organizers:
Jr-Shin Li and Shen Zeng
Department of Electrical and Systems Engineering
Washington University in St. Louis
St. Louis, MO, USA

Abstract:
A wide range of highly relevant problems found in nature, engineering, as well as societal structures are often plagued with overwhelmingly complex dynamical components and structures that are beyond the reach of current systems analysis and control design principles. A common thread of these very challenging problems is the pervasive theme of having large numbers of highly interacting dynamic parts. As a result, interest in cutting-edge analysis, estimation and control algorithms, and technologies suitable for these emerging sophisticated dynamical systems have seen stellar growth in recent years. A very promising approach that is rapidly gaining in interest and importance over the recent years is based on the idea of leveraging recent advances in data science and digital technology. Indeed, in many scientific domains data are becoming increasingly abundant, and easy to access or generate, while analytical models often remain elusive.

This workshop offers a survey of emerging techniques and research problems in this highly exciting field centered around data-driven computational methodologies to tackle control theory’s biggest open challenges related to highly nonlinear or very large-scale phenomena. Emphasis will be placed on both recent theoretical developments and emerging applications at the interface between systems science, data science, machine learning, physics, neuroscience, and biology. We will introduce state-of-the-art methods for both theoretical and data-driven investigations of fundamental properties of complex dynamical systems from measured or simulated data, including the problems of extracting governing equations or different relevant spatiotemporal structures, uncovering topological and geometric properties of the state space, as well as the introduction of novel controller and observer design paradigms. Moreover, several open problems and opportunities for further fruitful collaborative efforts in this emerging field at the intersection of systems and control theory, data science, statistics, and machine learning will be articulated and discussed.

Session Format:
The session will consist of a series of 40-minute presentations (with a 5-minute Q&A at the end) by the organizers and leading experts in the field. The workshop will conclude with an open dialogue between participants with the aim of engaging attendees in a lively discussion. We will strive to make the presentation material of the workshop available to the attendees for reference after the workshop.

Tentative schedule:

Time Name Affiliation
09:00 –09:10 Jr-Shin Li & Shen Zeng (Welcoming Remarks) Washington University in St. Louis
09:10 –09:50 Shen Zeng Washington University in St. Louis
09:50 –10:30 Debdipta Goswami and Derek A. Paley University of Maryland, College Park
10:30 – 11:00                                                     Coffee break
11:00 –11:40 Jr-Shin Li Washington University in St. Louis
11:40 –12:20 Paul Bogdan University of Southern California
12:20 – 01:50                                                     Lunch break
01:50 –02:30 Bethany Lusch Argonne National Laboratory
02:30 –03:10 Enoch Yeung University of California, Santa Barbara
03:10 – 03:40                                                    Coffee break
03:40 –04:20 Anne Romer and Frank Allgöwer University of Stuttgart
04:20                                          Discussion & Conclusions

 

Uncovering novel systems analysis and design principles through particle-based considerations
(40 minutes)

Shen Zeng
Department of Electrical and Systems Engineering
Washington University in St. Louis
St. Louis, MO, USA

Abstract
In the past decades, modeling and control were mostly concerned with exclusively one dynamical system with relatively mild complexity, which allowed for a highly successful systems theoretic treatment by purely analytical methods. However, recent years have witnessed a significant shift towards far more complex and large-scale dynamical systems in virtually all of the applied sciences, in which a traditional analytical approach is infeasible. This trend highlights the need for the exploration and development of novel systems analysis and design principles that are specifically applicable to complex and large-scale dynamical systems. In this talk, I will first introduce the very fruitful approach associated with viewing a complex dynamical system in a more global fashion, i.e. in terms of its macroscopic behavior. After providing a rapid review of the corresponding theory of transport operators (which are the adjoints of the Koopman operators), I will describe recent developments of employing sample-based approaches to efficiently elucidate and compute important dynamical features in complex systems, such as invariant sets and measures, isochrons, as well as more systems theoretic features, such as global observability measures for nonlinear systems. In contrast to parametric approaches employing function libraries for describing the spatio-temporal patters to be computed, sample-based, or, nonparametric, approaches are often more flexible and computationally more efficient.

Bio:
Shen Zeng is an Assistant Professor in the Electrical and Systems Engineering Department at Washington University in St. Louis. He studied Engineering Cybernetics, Mechatronics, and Mathematics at the University of Stuttgart, where he also received a Ph.D. degree in 2016. His research interests are in systems and control theory with a focus on analytic, algebraic, and geometric methods, and more recently, computational, methods.

 

Koopman Based Control: Bilinearization, Controllability and Optimal Control of Control-Affine Nonlinear Systems (40 minutes)

Debdipta Goswami
Department of Electrical and Computer Engineering and ISR
University of Maryland
College Park, MD, USA

Derek A. Paley
Department of Electrical and Computer Engineering and ISR
University of Maryland
College Park, MD, USA

Abstract
Nonlinear systems are ubiquitous in real world applications, but the control design for them is not an easy task. Hence, methods are sought to transform a control-affine nonlinear system into linear or bilinear forms to alleviate the problem of nonlinear controllability and control design. While there are linearization techniques like Carleman linearization for embedding a finite-dimensional nonlinear system into an infinite-dimensional space, they depend on the analytic property of the vector fields and work only on polynomial space. The Koopman-based approach described here utilizes the Koopman Canonical Transform (KCT) to transform the dynamics and ensures bilinearity from the projection of the Koopman operator associated with the control vector fields on the eigenspace of the drift Koopman operator. The sufficient conditions for exact bilinearization are derived. Even if the conditions are not fully met, the approximate bilinearization can also be posed as an optimization problem. The resulting bilinear system is then subjected to controllability analysis using the Myhill semigroup method and Lie algebraic structures. Using the same Myhill semigroup structure, we also seek to prove the existence of an optimal control with the help of Pontryagin’s Principle.


Bio:

Debdipta Goswami is a doctoral candidate in the Department of Electrical and Computer Engineering and the Institute for Systems Research at the University of Maryland. He received the B.E. degree in Electronics and Telecommunication Engineering from Jadavpur University, India, and his MS degree in Electrical and Computer Engineering from the University of Maryland His current research interests include nonlinear estimation, filtering, uncertainty quantification and operator theoretic approach to dynamical systems.

Derek A. Paley is the Willis H. Young Jr. Professor of Aerospace Engineering Education in the Department of Aerospace Engineering and the Institute for Systems Research at the University of Maryland. Paley received the B.S. degree in Applied Physics from Yale University in 1997 and the Ph.D. degree in Mechanical and Aerospace Engineering from Princeton University in 2007. He is the recipient of the Yale University Henry Prentiss Becton Prize for Excellence in Engineering and Applied Science in 1997, the Princeton University Harold W. Dodds Honorific Fellowship in 2006, the National Science Foundation CAREER award in 2010, the Presidential Early Career Award for Scientists and Engineers in 2012, the University of Maryland E.
Robert Kent Teaching Award for Junior Faculty in 2014, and the AIAA National Capital Section Engineer of the Year in 2015. Paley’s research interests are in the area of dynamics and control, including cooperative control of autonomous vehicles, adaptive sampling with mobile networks, and spatial modeling of biological groups. Paley is Associate Fellow of the American Institute of Aeronautics and Astronautics and Senior Member of the Institute of Electrical and Electronics Engineers. He serves as Associate Editor of AIAA Journal of Guidance, Control, and Dynamics.

 

Topological and Geometrical Data-Driven Learning and Embedding for Dynamical Systems and Controls (40 minutes)

Jr-Shin Li
Department of Electrical and Systems Engineering
Washington University in St. Louis
St. Louis, MO, USA

Abstract
Complex systems in which multiple agents affect each other dynamically are prevalent in nature and human society in different scales, such as neurons in the brain, bees in a hive, and human beings in a social network. Undesirable behavior of such systems, in the form of disease, economic collapse, rumor spreading, and social unrest, has generated considerable interest in understanding the dynamic structures of and devising ways to control complex dynamic networks. In many scientific domains, valid and precise mathematical models that describe complex system dynamics are often elusive; however, measurement data of the systems are abundant. Extracting dynamics of a large complex system from high-dimensional, noisy data is then becoming a central challenge in diverse areas of science and engineering. To date, reliable and efficient methods for the recovery of system dynamics or network topology remain a challenge due to the tremendous scale of emerging systems (e.g., brain, biological, and social networks) and the inherent nonlinearity within and between individual units. These obstacles also form a bottleneck for analyzing and engineering the dynamic structures (e.g., synchrony and clustering) or, further, for controlling the collective behavior in such complex networks. In this talk, a unified data-driven approach to decoding temporal structures of a dynamical system or time-varying topology of a complex network from its measured data will be presented. Novel topological and geometrical methods for the construction of local and global embeddings of high-dimensional data to low-dimensional manifolds will be introduced. These methods reveal hidden topological structures in large data sets, and identify the state space and characterize the dynamic modes and transition behavior of the underlying dynamical system that generates the data. Applications of the presented network inference, dimensionality reduction, and control techniques to diverse experimental systems, ranging from cellular networks to chemical interactions, will be illustrated. Future directions in the area of topological data science for systems and controls will be discussed.

Bio:
Jr-Shin Li is Professor of Systems Science and Mathematics in the Department of Electrical and Systems Engineering at Washington University in St. Louis, where he also holds a joint appointment in the Division of Biology & Biomedical Sciences since he joined Washington University in 2006. Dr. Li received a B.S. and an M.S. from National Taiwan University, and a Ph.D. in Applied Mathematics from Harvard University in 2006. His research interests lie in the areas of systems, computational, and data sciences, and their applications to biology, neuroscience, quantum physics, brain medicine, and public health. He is a recipient of the NSF Career Award in 2008 and the AFOSR Young Investigator Award in 2010. He is currently Associate Editor of the SIAM Journal on Control and Optimization (SICON) and the IEEE Transactions on Control Systems Technology (TCST).

 

 

Compact yet Accurate Mathematical Modeling: New Mathematical Tools for Modeling, Analysis and Optimization of Complex Systems (40 minutes)

Paul Bogdan
Ming Hsieh Department of Electrical Engineering – Systems
University of Southern California
Los Angeles, CA, USA

Abstract
From gene expression templates resulting from gene regulatory interdependencies, and brain activity motifs emerging from specific cognitive behavior, to congestion levels in communication networks, complex interdependent systems display multi-scale spatio-temporal patterns that are frequently classified as non-linear, non-Gaussian, non-ergodic, non-Markovian and/or fractal. Understanding the sources of non-linearity and exploiting the observed spatio-temporal fractality remains a major challenge not only for constructing dynamic causal models but also for identifying the graph structure and prediction of complex systems. Starting from these challenges, we discuss a new mathematical strategy for constructing compact accurate mathematical models of complex systems dynamics. Aiming to capture causal effects and to understand the non-linearity structure of complex interdependence systems, we investigate the statistics of the magnitude increments and the inter-event times of processes in the framework of non-extensive statistical physics and define a new learning strategy. The goal of maximizing the predictive capability of the identified (learned) model leads to a multi-fractional order nonlinear partial differential equation for the probability to find the system in a specific state at one time. This generalized probabilistic approach allows to construct multi-fractional dynamical models for complex interdependent dynamics and define new graph topology inference methods. We investigate and demonstrate the capabilities of this new mathematical framework in the context of brain-muscle interdependent networks.

Bio:
Paul Bogdan received his Ph.D. degree in Electrical and Computer Engineering from Carnegie Mellon University, Pittsburgh. He is an assistant professor in the Ming Hsieh Department of Electrical Engineering at University of Southern California. His work has been recognized with a number of distinctions, including the 2012 A.G. Jordan Award from the Electrical and Computer Engineering Department, Carnegie Mellon University for outstanding Ph.D. thesis and service, the 2012 Best Paper Award from the Networks-on-Chip Symposium (NOCS), the 2012 D.O. Pederson Best Paper Award from IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, the 2012 Best Paper Award from the International Conference on Hardware/Software Codesign and System Synthesis (CODES+ISSS), the 2013 Best Paper Award from the 18th Asia and South Pacific Design Automation Conference, and the 2009 Roberto Rocca Ph.D. Fellowship. His research interests include performance analysis and design methodologies for multicore systems, the theoretical foundations of cyber-physical systems, the modeling and analysis of bio-inspired computing, and the applications of statistical physics to biological systems and regenerative medicine.

 

Deep learning for universal linear embeddings of nonlinear dynamics (40 minutes)

Bethany Lusch
Argonne National Laboratory
Lemont, IL, USA

Abstract
Nonlinearity gives rise to diverse dynamical behaviors across science and engineering. While analysis and control of linear systems are well-understood, there is no general framework for nonlinear systems. According to Koopman theory, there exist coordinate transformations that make strongly nonlinear dynamics approximately linear. Such transformations have the potential to enable nonlinear prediction, estimation, and control using linear theory. However, they are challenging to find. This work leverages deep learning to discover representations of appropriate coordinate transformations from data. Our transformations are parsimonious and interpretable by construction, embedding the dynamics in a low-dimensional space. We identify nonlinear coordinates on which the dynamics are globally linear using a modified autoencoder. We also generalize Koopman representations to include a ubiquitous class of systems with continuous spectra while maintaining a compact and efficient embedding. Thus, we benefit from the power of deep learning, while retaining the physical interpretability of Koopman embeddings. 

Bio:
Bethany Lusch has a B.S. degree in mathematics from the University of Notre Dame and both an M.S. and Ph.D. in applied mathematics from the University of Washington. She is currently an Assistant Computer Scientist at the Leadership Computing facility at Argonne National Laboratory. Her research interests include machine learning, dynamical systems, optimization, scientific computing, and high performance computing.

 

 

Structured and Deep Dynamic Mode Decomposition for Discovery Problems in Synthetic and Systems Biology (40 minutes)

Enoch Yeung
Department of Mechanical Engineering
University of California, Santa Barbara
Santa Barbara, CA, USA

Abstract
A pervasive challenge in synthetic and natural gene networks is the absence of canonical models, for forecasting dynamical behavior and modeling emergent phenotypes. We consider the problem of extracting governing equations for synthetic genetic circuits from a range of biological measurements, including bulk cell culture measurements, transcriptomic measurements, as well as distributional measurements of gene expression. In scenarios where measurements exhibit high temporal resolution and low depth or penetration of whole-cell state, we show the efficacy of deep dynamic mode decomposition, an algorithm that combines deep learning with the Koopman operator framework for discovery of Koopman observables and governing equations with countable spectra. In the case where measurements are sparse in time, but exhibit high spatial depth (covering the whole transcriptome), we introduce sparse and structured dynamic mode decomposition algorithms, which provide best-case estimates for the most salient interactions observed among genes. We show recent extension of these algorithms to address heterogeneous noise distributions across biological time and across the genome. 

Bio:
Enoch Yeung has a B.S. in Mathematics from Brigham Young University, magnua cum laude with university honors and a Ph.D. in Control and Dynamical Systems from the California Institute of Technology. He has worked on several multi-institutional collaborative synthetic biological research programs including the DARPA Living Foundries program, the NSF Molecular Programming Project, and the AFOSR Biological Research Initiative. He is currently an assistant professor in the Department of Mechanical Engineering, the Biomolecula Science and Engineering Program, and the Center for Control, Dynamical Systems, and Computation. His research interests center in learning algorithms for dynamical systems, experimental and computational synthetic biology, and control and dynamical systems theory. He is the recipient of an National Defense Science and Engineering Graduate Fellowship, National Science Foundation Graduate Fellowship, Kanel Foundation Fellowhsip, an ACC Best Presentation Session Award, two PNNL Outstanding Performance Awards, and a Charles Lee Powell Foundation Fellowship.

 

 

Sampling schemes for data-driven inference of system properties (40 minutes)

Anne Romer
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
With the rising amount of data, there has been an increasing interest in what is referred to as data-driven controller design. One complementary approach to this direct controller design from data is to learn and analyze certain dissipation inequalities from data first since they allow for the direct application of well-known feedback theorems for controller design. Hence, by learning such system-theoretic input-output properties from data, we obtain insights to the a-priori unknown system, we are not bound to a certain controller structure beforehand while still providing control theoretic guarantees for the closed-loop behavior. In this context, there exist different approaches to determine these system properties from data with guarantees. In this talk, we will focus on sampling strategies to iteratively determine the operator gain, passivity measures and conicity of linear time-invariant systems, whose input-output map remains undisclosed. These sampling strategies are based on gradient dynamical systems and saddle point flows, where the respective gradients can be computed from only input-output data.


Bio:

Anne Romer received the B.S. degree in Engineering Cybernetics from the University of Stuttgart and holds both an M.S. in Engineering Science and Mechanics from the Georgia Institute of Technology and an M.S. in Engineering Cybernetics from the University of Stuttgart. During her studies, she spent one semester as a visiting student at the Tongji University in Shanghai. She is currently a research and teaching assistant at the Institute for Systems Theory and Automatic Control pursuing a Ph.D. degree within the International Max Planck Research School for Intelligent Systems. Her research interests include data-driven systems analysis and control.

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 of the International Federation of Automatic Control IFAC.