Data-driven Framework for Stability, Performance, and Safety Using Linear Transfer Operators

April 28, 2023 11:00 am – 12:00 pm

Location: TSRB 132

Umesh Vaidya


Mechanical Engineering

Clemson University


This talk will present results on applying linear transfer operator theory involving Perron-Frobenius and Koopman operators for data-driven control problems. In the first part of this talk, I will show the results of developing Koopman theory for control dynamical systems. One of the main challenges in using Koopman theory for control problems arises due to the bilinear lifting of the control dynamical system. We circumvent the bilinear lifting problem by establishing a connection between the spectrum of the Koopman operator and the Hamilton Jacobi (HJ) equation. We show that the solution to the HJ equation can be extracted from the spectrum of the Koopman operator. The HJ equation is the cornerstone of various problems in control theory, including optimal control, robust control, input-output analysis, dissipativity theory, and reachability/safety analysis. The connection between the Koopman spectrum and the HJ solution opens the possibility of exploiting the Koopman spectrum for various control problems. One of the main advantages of using the Koopman theory is that the Koopman operator and its spectrum can be approximated using data. We present novel approaches for computing the Koopman spectrum from data, thereby leading to systematic convex optimization-based methods for solving the HJ equation with application to optimal control design and input-output analysis of a nonlinear system.

In the second part of this talk, we will present results involving the Perron-Frobenius operator for the convex formulation of the optimal control problem with safety constraints. The convex problem is formulated over the space of densities defined only over the state space. The convex formulation is attractive for multiple reasons. First, the convex optimization problem can be constructed based on the data-driven approximation of the Koopman operator, dual to the Perron-Frobenius operator. Second, the convex incorporation of safety constraints allows us to provide a novel approach for the analytical construction of density functions for navigation. The proposed density function is used for navigation in a complex environment and high dimensional configuration space. The proposed construction overcomes the problem associated with navigation based on navigation functions, which are known to exist but challenging to construct, and potential functions that suffer from the existence of local minima. Finally, we demonstrate the application of the developed results for controlling the robotic system and vehicle autonomy.


Dr. Umesh Vaidya received a Ph.D. in Mechanical Engineering from the University of California at Santa Barbara, Santa Barbara, CA, in 2004. He was a research engineer at the United Technologies Research Center (UTRC), East Hartford, CT. Dr. Vaidya is a Professor of Mechanical Engineering at Clemson University, SC. Before joining Clemson University in 2019, and since 2006, he was a faculty member with the Department of Electrical and Computer Engineering at Iowa State University, Ames, IA. He is the recipient of the 2012 National Science Foundation CAREER award. His current research interests include dynamical systems and control theory with application to power systems, robotic systems, and vehicle autonomy.

What makes learning to control easy or hard?

April 14, 2023 11:00 am – 12:00 pm

Location: TSRB auditorium

Nikolai Matni

Assistant Professor

Department of Electrical and Systems Engineering

University of Pennsylvania


Designing autonomous systems that are simultaneously high-performing, adaptive, and provably safe remains an open problem.  In this talk, we will argue that in order to meet this goal, new theoretical and algorithmic tools are needed that blend the stability, robustness, and safety guarantees of robust control with the flexibility, adaptability, and performance of machine and reinforcement learning.  We will highlight our progress towards developing such a theoretical foundation of robust learning for safe control in the context of two case studies: (i) characterizing fundamental limits of learning-enabled control, and (ii) developing novel robust imitation learning algorithms with finite sample-complexity guarantees.  In both cases, we will emphasize the interplay between robust learning, robust control, and robust stability and their consequences on the sample-complexity and generalizability of the resulting learning-based control algorithms.


Nikolai Matni is an Assistant Professor in the Department of Electrical and Systems Engineering at the University of Pennsylvania, where he is also a member of the Department of Computer and Information Sciences (by courtesy), the GRASP Lab, the PRECISE Center, and the Applied Mathematics and Computational Science graduate group.  He has held positions as a Visiting Faculty Researcher at Google Brain Robotics, NYC, as a postdoctoral scholar in EECS at UC Berkeley, and as a postdoctoral scholar in the Computing and Mathematical Sciences at Caltech. He received his Ph.D. in Control and Dynamical Systems from Caltech in June 2016. He also holds a B.A.Sc. and M.A.Sc. in Electrical Engineering from the University of British Columbia, Vancouver, Canada. His research interests broadly encompass the use of learning, optimization, and control in the design and analysis of autonomous systems.  Nikolai is a recipient of the NSF CAREER Award (2021), a Google Research Scholar Award (2021), the 2021 IEEE CSS George S. Axelby Award, and the 2013 IEEE CDC Best Student Paper Award.  He is also a co-author on papers that have won the 2022 IEEE CDC Best Student Paper Award and the 2017 IEEE ACC Best Student Paper Award.

A Finite-Sample Analysis of Payoff-Based Independent Learning in Zero-Sum Stochastic Games

April 7, 2023 11:00 am – 12:00 pm

Location: TSRB auditorium

Dr. Zaiwei Chen

CMI postdoctoral fellow 

The Computing + Mathematical Sciences (CMS) Department 

California Institute of Technology


We study two-player zero-sum stochastic games, and propose a form of independent learning dynamics called Doubly Smoothed Best-Response dynamics, which combines a discrete and doubly smoothed variant of the best-response dynamics with temporal-difference (TD)-learning and minimax value iteration. The resulting dynamics are payoff-based,  convergent, rational, and symmetric among players.  Our main results provide finite-sample guarantees. In particular, we prove the first-known $\tilde{\mathcal{O}}(1/\epsilon^2)$ sample complexity bound for payoff-based independent learning dynamics, up to a smoothing bias. In the special case where the stochastic game has only one state (i.e., matrix games), we provide a sharper $\tilde{\mathcal{O}}(1/\epsilon)$ sample complexity. Our analysis uses a novel coupled Lyapunov drift approach to capture the evolution of multiple sets of coupled and stochastic iterates, which might be of independent interest.


Dr. Zaiwei Chen is currently a CMI postdoctoral fellow in The Computing + Mathematical Sciences (CMS) Department at California Institute of Technology, hosted by Dr. Adam Wierman and Dr. Eric Mazumdar. Zaiwei obtained a Ph.D. degree in Machine Learning, an M.S. degree in Mathematics, and an M.S. degree in Operations Research from Georgia Institute of Technology, where he was advised by Dr. Siva Theja Maguluri and Dr. John-Paul Clarke. Before that, Zaiwei obtained his B.S. degree in Electrical Engineering at Chu Kochen Honors College, Zhejiang University.

Zaiwei was a recipient of the Simoudis Discovery Prize, and was named a PIMCO Postdoctoral Fellow in Data Science in 2022. His Ph.D. thesis won the Sigma Xi Best Ph.D. Thesis Award, and was selected as a runner-up for the 2022 SIGMETRICS Doctoral Dissertation Award. Before that, Zaiwei received the ARC-TRIAD Student Fellowship in 2021, and was selected as as one of 7 nominees to represent Georgia Institute of Technology at the 2021 Schmidt Science Fellows Award Competition. A proposal based on his research received The IDEaS-TRIAD Research Scholarship in 2020.

Tunable Control Barrier Functions for Multi-Agent Safety via Trust Adaptation

March 31, 2023 11:00 am – 12:00 pm

Location: TSRB 509

Dimitra Panagou

Associate Professor

Department of Robotics

Department of Aerospace Engineering

University of Michigan


We will present some of our recent results and ongoing work on safety-critical control synthesis under state, time and input constraints, with applications to non-cooperative multi-agent systems and, time permitting, spacecraft control applications. The proposed framework aims to eventually develop and integrate adaptive, learning and control methods towards provably-correct and computationally-efficient mission synthesis for multi-agent systems in the presence of constraints and uncertainty.


Dimitra Panagou received the Diploma and PhD degrees in Mechanical Engineering from the National Technical University of Athens, Greece, in 2006 and 2012, respectively. In September 2014 she joined the Department of Aerospace Engineering, University of Michigan as an Assistant Professor. Since July 2022 she is an Associate Professor with the newly established Department of Robotics, with a courtesy appointment with the Department of Aerospace Engineering, University of Michigan. Prior to joining the University of Michigan, she was a postdoctoral research associate with the Coordinated Science Laboratory, University of Illinois, Urbana-Champaign (2012-2014), a visiting research scholar with the GRASP Lab, University of Pennsylvania (June 2013, Fall 2010) and a visiting research scholar with the University of Delaware, Mechanical Engineering Department (Spring 2009).

Dr. Panagou’s research program spans the areas of nonlinear systems and control; multi-agent systems and networks; motion and path planning; human-robot interaction; navigation, guidance, and control of aerospace vehicles. She is particularly interested in the development of provably-correct methods for the safe and secure (resilient) operation of autonomous systems in complex missions, with applications in robot/sensor networks and multi-vehicle systems (ground, marine, aerial, space). Dr. Panagou is a recipient of the NASA Early Career Faculty Award, the AFOSR Young Investigator Award, the NSF CAREER Award, and a Senior Member of the IEEE and the AIAA.

More details:

Information-Theoretic Approach to Gaussian Belief Space Path Planning for Minimum Sensing Navigation

February 10, 2023 11:00am – 12:00pm

Location: TSRB auditorium

Ali Reza Pedram


University of Texas at Austin


Motion planning and strategic sensing are inseparable problems for autonomous robots navigating in uncertain environments under perceptual resource constraints. In this talk, a new path planning methodology for a mobile robot in an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts will be discussed. In this framework, the desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a certain information-geometric distance function. The distance function introduced can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to solve the formulated shortest-path problem. The asymptotic optimality of the proposed path planning algorithm will also be discussed. A smoothing algorithm will be presented to remove the possible sharp turns, which are common in sampling-based planners, in the output of the proposed algorithm. Finally, simulation results will be presented demonstrating that the proposed method is effective in various robot navigation scenarios to reduce sensing costs, such as the required frequency of sensor measurements and the number of sensors that must be operated simultaneously.


Ali Reza Pedram received the B.Sc. degrees in mechanical engineering and applied physics from the Sharif University of Technology, Tehran, Iran, in 2015, and the M.S. degree in mechanical engineering from the Sharif University of Technology in collaboration with the Max Planck Institute for Intelligent Systems, Stuttgart, Germany, in 2017. He is currently working toward the Ph.D. degree in mechanical engineering with the University of Texas at Austin, Austin, TX, USA. His research interests include motion planning, information theory, stochastic control, and optimization.

Building Certifiably Safe and Correct Large-scale Autonomous Systems

November 11, 2022 11:00am – 12:00pm

Location: Technology Square Research Building 118 auditorium

Chuchu Fan

Assistant Professor

Department of Aeronautics and Astronautics



The introduction of machine learning (ML) and artificial intelligence (AI) creates unprecedented opportunities for achieving full autonomy. However, learning-based methods in building autonomous systems can be extremely brittle in practice and are not designed to be verifiable. In this talk, I will present several of our recent efforts that combine ML with formal methods and control theory to enable the design of provably dependable and safe autonomous systems. I will introduce our techniques to generate safety certificates and certified decision and control for complex autonomous systems, even when the systems have a large number of agents, follow nonlinear and nonholonomic dynamics, and need to satisfy high-level specifications.


Chuchu Fan an Assistant Professor in the Department of Aeronautics and Astronautics and LIDS at MIT. Before that, she was a postdoc researcher at Caltech and got her Ph.D. from the Electrical and Computer Engineering Department at the University of Illinois at Urbana-Champaign in 2019. She earned her bachelor’s degree from Tsinghua University, Department of Automation. Her group at MIT works on using rigorous mathematics including formal methods, machine learning, and control theory for the design, analysis, and verification of safe autonomous systems. Chuchu’s dissertation work “Formal methods for safe autonomy” won the ACM Doctoral Dissertation Award in 2020.

Geometric Characterization of H-property for Step-graphons

October 21, 2022 11:00am – 12:00 pm

Location: Technology Square Research Building 509

Xudong Chen

Assistant Professor

Department of Electrical, Computer, and Energy Engineering

University of Colorado Boulder


Graphon has recently been introduced by Lovasz, Sos, etc. to study very large graphs. A graphon can be understood as either the limit object of a convergent sequence of graphs, or, a statistical model from which to sample large random graphs. We take here the latter point of view and address the following problem: What is the probability that a random graph sampled from a graphon has a Hamiltonian decomposition? We have recently observed the following phenomenon: In the asymptotic regime where the size of the random graph goes to infinity, the probability tends to be either 0 or 1, depending on the underlying graphon. In this talk, we establish this “zero-one” property for the class of step-graphons and provide a geometric characterization.


Xudong Chen is an Assistant Professor in the Department of Electrical, Computer, and Energy Engineering at the University of Colorado Boulder. Prior to that, he was a postdoctoral fellow in the Coordinated Science Laboratory at the University of Illinois, Urbana-Champaign. He obtained the B.S. degree in Electronics Engineering from Tsinghua University, China, in 2009, and the Ph.D. degree in Electrical Engineering from Harvard University, Massachusetts, in 2014. He is an awardee of the 2020 Air Force Young Investigator Program, a recipient of the 2021 NSF CAREER award, and the recipient of the 2021 Donald P. Eckman award. His current research interests are in the area of control theory, stochastic processes, optimization, graph theory and their applications in modeling, analysis, control, and estimation of large-scale complex systems.

Stochastic Kolmogorov Systems and Applications

September 23, 2022 11:00 am – 12:00 pm

Location: 118 Auditorium, Technology Square Research Building

George Yin


Department of Mathematics

University of Connecticut


In this talk, we will present some of our recent work on stochastic Kolmogorov systems. The motivation stems from dealing with important issues of ecological and biological systems. Focusing on environmental noise, we aim to address such fundamental questions: “what are the minimal conditions for long-term persistence of a population, or long-term coexistence of interacting species”. Some optimal control problems are also examined. [The talk reports some of our joint works with  D.H. Nguyen, N.T. Dieu, N.H. Du, and N.N Nguyen.]


George Yin received the B.S. degree in mathematics from the University of Delaware in 1983, and the M.S. degree in electrical engineering and the Ph.D. degree in applied mathematics from BrownUniversity in 1987. He joined the Department of Mathematics, Wayne State University in 1987 and became Professor in 1996 and University Distinguished Professor in 2017. He moved to the University of Connecticut in 2020. His research interests include stochastic processes, stochastic systems theory, and applications. He was Chair of the SIAM Activity Group on Control and Systems Theory, and  was Co-chair of a number of conferences; he served on the Board of Directors of the American Automatic Control Council.  He is  Editor-in-Chief of SIAM Journal on Control and Optimization. He serves on (or served on) editorial boards of over 20 journals and book series including Automatica 1995-2011, IEEE Transactions on Automatic Control  1994-1998, and IEEE Control Systems Letters 2017-2019. He is a Fellow of IEEE, Fellow of IFAC, and  Fellow of SIAM.

In Memoriam: Dr. Radhakishan Sohanlal Baheti

Kishan Baheti speaking at the National Science Foundation.

This webpage is part of the memorial activities for Dr. Baheti at the 2022 American Control Conference.

Dr. Radhakishan Sohanlal Baheti, a pioneering member of the IEEE Control Systems Society (CSS), passed away on March 9, 2021 at the age of 76. He served as a program director for the Energy, Power, Control, and Networks Program in the Division of Electrical, Communications and Cyber Systems at the U.S. National Science Foundation (NSF), overseeing a broad spectrum of research areas in control theory, power systems, robotics, multiagent systems, and data science.

Dr. Baheti received the B.S. and M.S. degrees in electrical engineering in India from Visvesvaraya Regional College of Engineering, Nagpur, and Birla Institute of Technology and Science, Pilani, respectively. In 1970, he came to the United States and received an M.S. degree in information and computer science from the University of Oklahoma and a Ph.D. degree in electrical and computer engineering from Oregon State University. In 1976, Dr. Baheti joined the Control Engineering Laboratory of General Electric (GE) Corporate Research and Development Center in Schenectady, New York. His work focused on advanced multivariable control for jet engines, signal and image processing systems, computer-aided control system design, vision-based robots for precision welding, model-based fault identification, and parallel implementation of Kalman filters. Dr. Baheti and his colleagues received the IR-100 Award for the robotic welding vision system. During his tenure at GE, he organized a series of educational workshops for engineers that resulted in innovative product developments and enhanced university collaborations with GE.

In 1989, Dr. Baheti (or Kishan, as he was fondly known to his friends and colleagues) joined the NSF as a program director in the Division of Electrical, Communications, and Cyber Systems. For more than 30 years in this role, he was a tireless worker for the support of the entire control system community in the United States and abroad. Among his many seminal contributions were the development of NSF initiatives on cyberphysical systems, semiconductor manufacturing, the National Robotics Initiative, and the NSF Electric Power Research Institute (NSF-EPRI) Initiative on Intelligent Control.

In addition to his usual directorial duties in control engineering, Kishan was also involved in many multidisciplinary research initiatives:

Pramod Khargonekar:

I had the good fortune to work with Kishan closely from 2013 to 2016 during my tenure as assistant director for the Engineering Directorate at NSF. I saw him directly in action as he worked with colleagues from many other divisions to develop numerous new programs in smart grids, wireless communications, sensors, micro and nano systems, science of learning, and dynamics and control of biological and medical systems. Without his creative energy and people skills, our community would have missed many of these opportunities.

Kishan served as an associate editor for IEEE Transactions on Automatic Control. He was a member of the CSS Board of Governors, chair for the Public Information Committee, and Awards chair for the American Automatic Control Council. He received the Distinguished Member Award from the IEEE CSS. His other awards include the 2012 Robert H. Janowiak Outstanding Leadership and Service Award from the Electrical and Computer Engineering Department Heads Association (ECEDHA), Outstanding Men of America Award, and multiple service awards from the NSF. In 1997, he was elected Fellow of IEEE.

Kishan is best known for his pioneering advocacy for the control systems research community in the United States through his continuous collaboration with IEEE CSS and IEEE Power & Energy Society. He was instrumental in bringing researchers and educators in these communities together through a series of workshops, tutorials, special sessions, and industry engagement events held at leading conferences. From 2013 to 2019, he organized six international workshops on distributed energy management systems that brought together leading international researchers in smart grids from the United States, Japan, Germany, Norway, and India. In recent years, he also led NSF efforts in the 10 big ideas on harnessing the data revolution, connecting researchers in control theory with those in machine learning and data science. His openness to new directions, new areas of research, and community building are deemed as legendary by all his peers.

Aranya Chakrabortty:

Kishan played a leading role in shaping the intellectual direction of our field, and a number of us got our very first grants through Kishan’s programs at NSF. He was the biggest cheerleader there is for young researchers in our community … Looking at the volume of work that Kishan has done in his life makes me feel that if I can even rise up to his knees, I would consider that to be an achievement of a lifetime.
Participants at the System Identification Workshop, GE CR&D, June 5–6, 1986. Front middle: Kishan Baheti and Lennart Ljung; second row: Howard Kaufman (far left) and Joe Chow (second from right).  

Kishan was an avid long-distance runner, a marathoner, an ardent yoga practitioner, and a voracious reader. He frequently participated in local run events in the Washington, D.C. area as well as in the Boston Marathon.

Kishan Baheti running in the Boston Marathon

These many professional accomplishments and impacts only capture a partial picture of Kishan Baheti. While he was a brilliant and successful professional, his personal qualities made him a great human being and a friend to many. He was kindhearted and magnanimous. He had deep compassion for fellow human beings. He had a tremendous capacity to see the positive and good in each and every situation, no matter how difficult. He believed in others and helped them believe in themselves. He had that rare quality: wisdom. As a part of the control systems research community, we are all deeply grateful for what we have received from our beloved Kishan. We will miss him sorely and will cherish his memories forever.

May Kishan rest in peace.

The material comes from Control Systems Magazine, Aug 2021, Page 99-102.

Please feel free to leave a message at the bottom of this page.

Online Optimization and Control using Black-Box Predictions

April 19, 2022 11:00 am – 12:00 pm

Location: Instructional Center 105

Also live streamed at

Zoom Meeting ID: 968 1345 6832

Adam Wierman




Making use of modern black-box AI tools is potentially transformational for online optimization and control. However, such machine-learned algorithms typically do not have formal guarantees on their worst-case performance, stability, or safety. So, while their performance may improve upon traditional approaches in “typical” cases, they may perform arbitrarily worse in scenarios where the training examples are not representative due to, e.g., distribution shift or unrepresentative training data. This represents a significant drawback when considering the use of AI tools for energy systems and autonomous cities, which are safety-critical. A challenging open question is thus: Is it possible to provide guarantees that allow black-box AI tools to be used in safety-critical applications? In this talk, I will introduce recent work that aims to develop algorithms that make use of black-box AI tools to provide good performance in the typical case while integrating the “untrusted advice” from these algorithms into traditional algorithms to ensure formal worst-case guarantees. Specifically, we will discuss the use of black-box untrusted advice in the context of online convex body chasing, online non-convex optimization, and linear quadratic control, identifying both novel algorithms and fundamental limits in each case.


Adam Wierman is a Professor in the Department of Computing and Mathematical Sciences at Caltech. He received his Ph.D., M.Sc., and B.Sc. in Computer Science from Carnegie Mellon University and has been a faculty at Caltech since 2007. Adam’s research strives to make the networked systems that govern our world sustainable and resilient. He is best known for his work spearheading the design of algorithms for sustainable data centers and his co-authored book on “The Fundamentals of Heavy-tails”. He is a recipient of multiple awards, including the ACM Sigmetrics Rising Star award, the ACM Sigmetrics Test of Time award, the IEEE Communications Society William R. Bennett Prize, multiple teaching awards, and is a co-author of papers that have received “best paper” awards at a wide variety of conferences across computer science, power engineering, and operations research.