Titles, Abstracts, and Slides

The turnpike property is an asymptotic-stability-like property of solutions of optimal control problems. It was first observed in the 1920s and 1930s by Ramsey and von Neumann and extensively studied in the 1960s and 1970s in mathematical economy. In recent years, it has attracted a lot of renewed attention in the Model Predictive Control (MPC) community on the one hand and in the Partial Differential Equation (PDE) control community on the other hand.

In this lecture we start by explaining the turnpike property with simple examples. We will then turn to establishing relations to classical properties in systems theory and optimal control, such as dissipativity, detectability, and sensitivity. In this context, we will also explain recent results for PDE-governed optimal control problems. Finally, we will present new results on the existence of global and local turnpike properties for discounted optimal control and first results for the turnpike property in stochastic linear quadratic optimal control problems. 

Biography 

Lars Grüne has been a Professor of Applied Mathematics at the University of Bayreuth, Germany, since 2002. He received his Diploma and Ph.D. in Mathematics in 1994 and 1996, respectively, from the University of Augsburg and his habilitation from the J.W. Goethe University in Frankfurt/M in 2001. He held visiting positions at the Universities of Rome `Sapienza' (Italy), Padova (Italy), Melbourne (Australia), Paris IX - Dauphine (France) and Newcastle (Australia). Prof. Grüne was General Chair of the 25th International Symposium on Mathematical Theory on Networks and Systems (MTNS 2022), he is Editor-in-Chief of the journal Mathematics of Control, Signals and Systems (MCSS) and is or was Associate Editor of various other journals, including the Journal of Optimization Theory and Applications (JOTA), Mathematical Control and Related Fields (MCRF) and the IEEE Control Systems Letters (CSS-L). His research interests lie in the area of mathematical systems and control theory with a focus on numerical and optimization-based methods for nonlinear systems.  

(Talks 1)

For mechanical control systems we present the problem of linearization that preserves the mechanical structure of the system. We give necessary and sufficient conditions for the mechanical state-space-linearization and mechanical feedback-linearization using geometric tools, like covariant derivatives, symmetric product,  and the Riemann tensor, that have an immediate mechanical interpretation. In contrast with linearization of general nonlinear systems, conditions for its mechanical counterpart can be given for both, controllable and noncontrollable, cases. We illustrate our results by examples of linearizable mechanical systems. The talk is based on joint research with Marcin Nowicki (Poznan University of Technology, Poland). 

(Talks 2)

For a linear differential-algebraic equation, shortly DAE, a procedure called explicitation is proposed, which attaches to any linear DAE a linear control system defined up to a coordinates change, a feedback transformation, and an output injection. We show that the classical Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of control systems have a perfect correspondence and that their invariants are related. We thus connect the geometric analysis of linear DAEs with the classical geometric linear control theory. Then we propose a concept called internal equivalence for DAEs and discuss its relation with internal regularity, i.e., the existence and uniqueness of solutions.

In the second part of the talk, we propose an analogous theory for nonlinear DAEs. We revise the geometric reduction method for obtaining solutions of nonlinear DAEs and formulate an implementable algorithm to realize that method. A procedure called explicitation with driving variables is proposed to connect nonlinear DAEs with nonlinear control systems and we show that the driving variables of an explicitation system can be reduced under some involutivity conditions.

Finally, due to the explicitation, we use some notions from nonlinear control theory to derive two nonlinear generalizations of the classical Weierstrass form known for linear DAEs. The talk is based on common research with Yahao Chen, Centrale Nantes, France. 

Biography 

Professor Witold Respondek was born in Poland. He received his Ph.D. degree form the Institute of Mathematics, Polish Academy of Sciences in 1981. He has had positions at the Technical University of Warsaw and at the Polish Academy of Sciences. Since 1994 he has been a professor of applied mathematics at the INSA de Rouen, France. General areas of his scientific interest are geometric methods in systems and control theory as well as geometric methods in differential equations. His research papers have been devoted to problems of linearization of nonlinear control systems, nonlinear observers, classification of control systems and vector distributions, dynamic feedback, applications of high-gain feedback to nonlinear systems, and systems invariant on cones. Recently he has been working on mechanical control systems and on flatness, with particular emphasis on systems with nonholonomic constraints, and on geometry of optimal control problems. He has been an associated editor of SIAM Journal on Control and Optimization, Applicationes Mathematicae, Central European Journal of Mathematics, and Journal of Geometric Mechanics. He is an editor of six books and author or co-author of more than 100 journal and conference papers. 

In this talk, we will work with the following crowd motion model: a population confined to a particular closed space, for example, a cinema room, is trying to exit the room in the minimal possible time. This population features a specific structure, in the sense that it is constituted of groups of individuals each one remaining in its moving set, where each group intends to minimize its effort to achieve this. We establish the corresponding necessary optimality conditions, therefore providing information on the set of optimal solutions to this problem.

To model this crowd motion problem, we will give an overview of optimal control, bilevel optimization, and the sweeping process. Some examples are provided as well.

Biography

Nathalie T. Khalil is a Scientific Researcher at the University of Porto, Portugal with the Department of Electrical and Computer Engineering. She received the B.Sc. degree in pure mathematics from the Lebanese University, Beirut Lebanon in 2012, the M.Sc. degree in mathematics and applications from the University of Rennes 1, Rennes France, in 2014, and the Ph.D. degree in optimal control and applications from the University of Western Brittany, Brest France, in 2017.  She was a visiting Ph.D. student at the University of Padua in Italy for the period 2015-2016 and a visiting researcher in 2022 at the Autonomous Metropolitan University in Mexico City. She was also a teaching assistant in France and Portugal. Her research interests include optimal control, non-smooth analysis, indirect computational techniques for problems in optimal control, and problems combining sweeping process with bilevel optimization theory. 

Quantum error correction (QEC) usually relies on static output feedback. It then corresponds to a classical controller with as input classical signals from quantum measurements, and as output also classical signals and parameterizing the quantum evolution of the physical system. QEC can also exploit the dissipation associated with the decoherence phenomenon called autonomous QEC in Physics community, it uses a stabilizing feedback scheme where the controller is a dissipative quantum auxiliary system. This talk focuses on the design of such quantum controllers. The dynamics are governed by the master quantum equations (differential equations of Gorini-Kossakowski–Sudarshan–Lindblad) governing the temporal evolution of the quantum states (density operator replacing, for a quantum system with decoherence, the wave function). The design and convergence analysis are based on averaging techniques (rotating wave approximations), singular perturbation methods (adiabatic elimination) and Lyapunov functions. An important special case, where the controller is a dissipative quantum harmonic oscillator coherently coupled to the system storing the quantum information, is detailed. Such autonomous QEC schemes are developed experimentally with superconducting quantum circuits to protect quantum states stored in harmonic oscillators (bosonic codes relying on, e.g., cat-qubits).

Biography

Pierre Rouchon is professor with the Centre Automatique et Systemes at Mines Paris,Universite PSL. He graduated from Ecole Polytechnique in 1983, has obtained a PhD in 1990 and an “habilitation à diriger des recherches” in 2000. From 1993 to 2005, he was associated professor at Ecole Polytechnique in Applied Mathematics. From 1998 to 2002, he was the head of the Centre Automatique et Systèmes. From 2007 to 2018, he was the chair of the department “Mathématiques et Systèmes” at Mines Paris PSL. Since 2015, he is a member of the Quantic Research team between Inria, Ecole Normale Supérieure de Paris and Mines Paris. His fields of interest include nonlinear control and system theory with applications to physical systems. His contributions include differential flatness and its extension to infinite dimensional systems, non-linear observers and symmetries, quantum filtering and feedback control. In 2017, he received the “Grand Prix IMT – Académie des sciences de Paris.” 

Analytical and numerical tools of optimal control theory (1) have found widespread applications in spin-based spectroscopy, imaging and in quantum technology (2). In the last decade, these tools not only provided pulse sequences of unprecedented quality and capabilities, but also new analytical and geometrical insight and a deeper understanding of pulse optimization problems. In addition to studies of the performance limits of individual pulses, e.g. for excitation or refocusing (3), the perspective has been widened to the excitation of multiple-quantum coherences (4), the design of cooperative ultra-broadband pulse sequences (5), and the design of entire relaxation dispersion (6) and decoupling (7) experiments for liquid-state NMR. Further quantum-control applications include solid-state NMR (8), electron spin resonance spectroscopy (8), magnetic resonance imaging (9), and mass spectrometry (10). Furthermore, new challenges for optimal control methods arise in quantum information processing platforms, such as superconducting qubits and cold atoms, which are being developed in the Munich Quantum Valley (MQV) initiative. Finally, advanced intuitive and highly interactive visualization techniques, such as the DROPS representation (11), provide a powerful approach to interactively and intuitively explore the dynamics of coupled spin systems in teaching and research.  

References

(1) N. Khaneja, R. Brockett, S. J. Glaser, Phys. Rev. A 63, 032308/1-13 (2001); N. Khaneja, S. J. Glaser, R. Brockett, Phys. Rev. A 65, 032301 (2002); N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, S. J. Glaser, J. Magn. Reson. 172, 296-305 (2005).  

(2) S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm, Eur. Phys. J. D 69, 279/1-24 (2015); C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm, Eur. Phys. J. Quantum Technology 9, 19/1-60 (2022). 

(3) A. Garon, S. J. Glaser, and D. Sugny, Phys. Rev. A 88, 043422 (2013); N. Jbili, K. Hamraoui, S. J. Glaser, J. Salomon, D. Sugny, Phys. Rev. A 99, 053415 (2019); L. Van Damme, Q. Ansel, S. J. Glaser, D. Sugny, Phys. Rev. A 95, 063403 (2017); L. Van Damme, Q. Ansel, S. J. Glaser, D. Sugny, Phys. Rev. A 98, 043421 (2018); Q. Ansel, S. J. Glaser, D. Sugny, J. Phys. A, 54, 085204 (2021). 

(4) S. S. Köcher, T. Heydenreich, Y. Zhang, G. N. M. Reddy, S. Caldarelli, H. Yuan, S. J. Glaser, J. Chem. Phys. 144, 164103 (2016).  

(5) M. Braun, S. J. Glaser, New J. Phys. 16, 115002 (2014); S. Asami, W. Kallies, J. C. Günther, M. Stavropoulou, S. J. Glaser, M. Sattler, Angew. Chem. Int. Ed. 57, 14498-14502 (2018), W. Kallies, S. J. Glaser, J. Magn. Reson. 286, 115-137 (2018). 

(6) F. Schilling, L. R. Warner, N. I. Gershenzon, T. E. Skinner, M. Sattler, S. J. Glaser, Angew. Chem. Int. Ed. 53, 4475-4479 (2014). 

(7) T. T. Nguyen, S. J. Glaser, J. Magn. Reson. 282, 142-153 (2017).  

(8) Z. Tosner, R. Sarkar, J. Becker-Baldus, C. Glaubitz, S. Wegner, F. Engelke, S. J. Glaser, B. Reif, Angew. Chem. Int. Ed. 57, 14514-14518 (2018); Z. Tosner, M. J. Brandl, J. Blahut, S. J. Glaser, B. Reif, Science Advances 7, eabj5913 (2021).  

(9) P. E. Spindler, P. Schöps, W. Kallies, S. J. Glaser, T. F. Prisner, J. Magn. Reson 280, 30-35 (2017); Q. Ansel, S. Probst, P. Bertet, S. J. Glaser, D. Sugny, Phys. Rev. A 98, 023425 (2018).  

(10) Q. Ansel, M. Tesch, S. J. Glaser, D. Sugny, Phys. Rev. A 96, 053419/1-9 (2017); E. Van Reeth, H. Ratiney, M. Tesch, D. Grenier, O. Beuf, S. J. Glaser, D. Sugny, J. Magn. Reson. 279, 39-50 (2017).  

(11) V. Martikyan, A. Devra, D. Guery-Odelin, S. J. Glaser, D. Sugny, Phys. Rev. A 102, 033104 (2020). V. Martikyan, C. Beluffi, S. J. Glaser, M. A. Delsuc, D. Sugny, Molecules 26, 2860 (2021). 

(12) A. Garon, R. Zeier, S. J. Glaser, Phys. Rev. A 91, 042122 (2015); D. Leiner, R. Zeier, S. J. Glaser, J. Phys. A: Math. Theor. 53, 495301 (2020); The SpinDrops app can be downloaded at spindrops.org. 

Biography 

Professor Steffen Glaser conducts research on the development of novel theories and methods in nuclear magnetic resonance (NMR) experiments, focusing, in particular, on the optimal control of spin systems with applications in structural biology, medical imaging, and quantum information processing.

After studying physics in Heidelberg, he conducted his doctoral research at the Max-Planck-Institute for Medical Research, earning his doctorate from the University of Heidelberg in 1987. Following a research stay at the University of Washington, Seattle, he completed his post-doctoral teaching qualification at the University of Frankfurt/Main (1993). He was appointed to his professorship at TUM in 1999. Since 2005, he has served as a speaker for international doctoral programs of the Elite Network of Bavaria (QCCC: Quantum Computing, Communication, and Control, 2005-2013 and ExQM: Exploring Quantum Matter, 2014-2022), which include research groups at TUM, LMU, Max Planck Institute of Quantum Optics and the Bavarian Academy of Sciences and Humanities. 

The presentation will introduce single-spin vector effective Hamiltonian theory (SV-EHT) and exact effective Hamiltonian theory (EEHT) methods with focus on analysis and systematic design of advanced magnetic resonance experiments. These tools provide highly accurate/exact descriptions of the effective Hamiltonian with detailed information on linear and bilinear components and their interplay in experiments coping with large spread in nuclear or electron spin parameters. Such information may be of great interest to understand and design of advanced experimental methods in liquid- and solid-state NMR, EPR, and DNP enhanced NMR spectroscopy. The effective Hamiltonian methods – and combinations with non-linear optimization and optimal control – will be demonstrated for liquid-state NMR isotropic mixing,1 solid-state NMR dipolar recoupling,1 and broadband DNP experiments.2

References

1. A. B. Nielsen and N. C. Nielsen, ”Accurate analysis and perspectives for systematic design of magnetic resonance experiments using single-spin vector and exact effective Hamiltonian theory ”, J. Magn. Reson. Open 12-13. 100064 (2022).

2. N. Wili, A. B. Nielsen, L. A. Völker, L. Schreder, N. C. Nielsen, G. Jeschke, and K. O. Tan, ”Designing Broadband Pulsed Dynamic Nuclear Polarization Sequences in Static Solids”, Science Adv. 8,  eabq0536 (2022).

Biography 

Niels Chr. Nielsen, professor, Director of Danish Center for Ultrahigh-Field NMR Spectroscopy, Aarhus University. Born 1962. M.Sc. 1987, Ph.D. in 1990, Aarhus University, Denmark. Professor at Aarhus University 1999 and head of bioNMR activities. Cofounder, vice-director and later director of Interdisciplinary Nanoscience Center (iNANO) at Aarhus University 2002-2013, Director for the “Danish National Research Foundation Center for Insoluble Protein Structures (inSPIN)” 2005-2013, Dean of the Faculty of Science and Technology at Aarhus University 2013-2019. CTO at NanoNord A/S from 2013. Member of numerous boards and councils. Around 285 peer-reviewed publications, recipient of several awards and honors. Research interests are focused on the development and application of novel magnetic resonance techniques and instrumentation (NMR, MRI, EPR, DNP) to provide information about the composition, structure, dynamics, and function of materials and biological systems.

Reinforcement Learning (RL) can be viewed as a collection of techniques for solving Markov Decision Problems (MDPs) when the dynamics of the MDP are unknown.  Several algorithms such as Temporal Difference Learning and Q-Learning are widely used to solve RL problems, either exactly or approximately.  These algorithms are iterative, and the proofs that they converge are often not very intuitive.  My contention is that Stochastic Approximation (SA) in a variety of manifestations can be used to provide a unified approach to establishing the convergence of many such RL algorithms.  Traditional approaches to studying SA are based on the so-called ODE method, wherein it is shown that the sample paths of the SA algorithm "converge" to the deterministic trajectories of an associated ODE.  I will present an alternate approach based on the convergence theory for martingales, and Lyapunov stability theory.  This slightly odd mixture not only enables us to derive simple proofs, but also to eliminate some "technical" but unverifiable conditions, and replace them by simple algebraic conditions. 

Biography 

Mathukumalli Vidyasagar was born in Guntur, Andhra Pradesh, India on 29 September 1947.  He received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from the University of Wisconsin, Madison, in 1965, 1967 and 1969 respectively.  Between 1969 and 1989, he taught in Canada and the United States. In 1989 he returned to India and set up the Centre for Artificial Intelligence and Robotics, the first AI lab in India. In 2000 he moved to Tata Consultancy services, and in 2009 he joined the University of Texas at Dallas.  Since 2018, he has been associated with IIT Hyderabad, where he is now a National Science Chair.

Vidyasagar has received several honors and awards in recognition of his research, including the IEEE Control Systems Technical Field Award, and Fellowship in The Royal Society.  He is the author of 13 books and 160 journal papers.  His current research interest is reinforcement learning. 

Louis Poinsot's elegant construction for visualizing the changing orientation of a freely rotating rigid body using the mental picture of a body-fixed ellipsoid rolling without slipping on a fixed invariant plane or a "body" cone rolling without slipping on a stationary "space" cone are well known to anybody who has taken a classroom course on rigid-body dynamics. Less well known is a more general result appearing in Poinsot's memoir titled "Outlines of a New Theory of Rotatory Motion", which states that any arbitrary rotational motion between two frames can be realized through the motion of a cone fixed to one frame rolling without slipping on a second cone fixed to the other frame. We will show how this largely ignored observation can be used to improve known results on attitude reconstruction. Attitude reconstruction is the problem of reconstructing the relative orientation between two frames from continuous-time observations of a common vector made from both frames. Although the attitude reconstruction problem has connections to concepts such as holonomy, parallel transport, and curvature, we will use nothing more than elementary matrix-vector algebra and calculus in this talk. We will also get introduced to classical results such as the Goodman-Robinson theorem, the Rodrigues-Hamilton theorem, and Donkin's theorem.

Biography

Sanjay P. Bhat received the B.Tech. degree in aerospace engineering from the Indian Institute of Technology, Bombay, in 1992, and the M.S. and Ph.D. degrees in aerospace science from the University of Michigan, Ann Arbor, in 1993 and 1997, respectively. He taught at the Department of Aerospace Engineering, Indian Institute of Technology, Bombay, for ten years before joining TCS Research, where he leads a team of researchers working on applying learning techniques to sequential decision-making problems. His research interests include stability theory, nonlinear systems theory, dynamics and control of rotational motion, stochastic processes, and bandit algorithms.

Controlling nonlinear systems is a challenging problem that is traditionally addressed by linearizing the system at different operating points,  or through advanced methods such as Model Predictive Control (MPC). However, in line with the modern trend of using Machine Learning to design autonomous systems, Reinforcement Learning (RL) has the potential to solve complex control system problems using deep neural networks. 

In this workshop, we will walk through the basics of Reinforcement Learning for Controls using MATLAB and Simulink. We will cover the basic concepts, including neural networks, set up the environment models, and define the reward structure to shape the learning process. 

Biographies

Dr. Dhruv Chandel is a Senior Team Lead with the Education Team at MathWorks, the creators of MATLAB and Simulink software. This team works with top universities, government bodies, and industries worldwide to support engineering education and research. Dhruv has more than ten years of experience in Numerical Simulations, Control System Design, Robotics and Artificial Intelligence. Previously, he worked as a researcher in academia, including four years working with a startup renewable energy company based out of London. Dhruv earned his Master’s degree in Robotics and a Ph.D. in Renewable Energy from the University of Bath, UK.

Dr. Pranav Lad is a Customer Success Engineer at MathWorks, based out of Pune. He works closely with academic institutions in order to help accelerate the pace of research and to improve learning outcomes. His technical expertise lies in the field of vibrations, nonlinear dynamics,

robotics, and machine learning. He completed his master's and a doctorate in Mechanical Engineering from IIT Bombay. He has authored various research papers in international journals and conference proceedings. While working as a research assistant at IIT Bombay, he interacted with various industries for consultation. Prior to that, he received his Bachelor’s from the University of Pune.