Invited Speakers

Abstract: Given a control system on a smooth manifold M, any admissible control function generates a flow, i.e. a one-parametric family of diffeomorphisms of M. We give a sufficient condition for the system that guarantees the existence of an arbitrary good uniform approximation of any isotopic to the identity diffeomorphism by an admissible diffeomorphism and provide simple examples of control systems on R^n, T^n and S^2 that satisfy this condition. This work is motivated by the deep learning of artificial neural networks treated as a kind of interpolation techniques.

Homepage: https://people.sissa.it/~agrachev/

Short biography

Born: 1952.

Current position: Full Professor, SISSA, Trieste, Italy

Education: PhD, Moscow State University 1977. Doctor of Science, Steklov Mathematical Institute 1989.

Carrier:

-) All-Union Institute for Scientific Information (VINITI), Moscow, Russia, 1977-1992. Positions: researcher, senior researcher, leading researcher.

-) Steklov Mathematical Institute, Moscow, Russia, 1992–present. Positions: leading researcher, external collaborator.

-) Moscow State University, Department of Mechanics and Mathematics, 1989-1997. Positions: associate professor, full professor.

-) International School for Advanced Studies (SISSA), Trieste, Italy, 2000–present. Position: full professor.

-) Head of the research project “Geometric control theory and analysis on metric structures” supported by the Russian Federation, 2013-2015.

-) INRIA International Chair, 2020-2024.

Awards and honors:

-) Soviet Academy of Sciences Award in Mathematics, 1989.

-) Invited Speaker at the International Congress of Mathematicians ICM-94 in Z ̈urich, Switzerland.

-) Member of the Nevanlinna Prize Committee of the International Mathematical Union for ICM 2002 in Beijing, China.

-) Panel core member of the International Mathematical Union for ICM-2010 in Hyderabad, India.

Supervisor of 29 PhD students.

Author of more than 150 journal papers and 3 book.

Abstract: It is well known that a continuous feedback stabilization on an attractor is often impossible because of the mismatch of the topologies of the attractor and the configuration space of the system. I will discuss the implications on the topology of the locus of discontinuity of the feedback, and some examples motivated by control of robotic swarms.

Homepage: https://publish.illinois.edu/ymb/

Short biography

Yuliy Baryshnikov graduated as an applied mathematician from Russian University of Transport (MIIT) in Moscow, then worked till 1990 at the Institute of Control Sciences named after Academician Trapeznikov (IPU).

He spent the next decade in Germany, the Netherlands and France, first as Alexander von Humboldt research fellow, then as a Habilitandedstipendiat of the DFG, and, finally, as a professor at the Mathematical department of UVSQ (Université de Versailles Saint-Quentin-en-Yvelines), France.

In 2001 he joined Bell Labs (then at Lucent Technologies), USA, first as a Member of technical staff, later as a department head. He has been with University of Illinois, USA, since 2011.

Yuliy's research interests cover applied topology, complex geometry in analytic combinatorics, applied probability, dynamical systems, nonlinear control, social choice theory and institutional perfidy.

Abstract: Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the Grushin plane. They are generalized Riemannian structures for which the vectors of a local orthonormal frame can become parallel. Under the 2-step assumption the singular set Z, where the structure is not Riemannian, is a 1D embedded submanifold. While approaching the singular set, all Riemannian quantities diverge. A remarkable property of these structures is that the geodesics can cross the singular set without singularities, but the heat and the solution of the Schrödinger equation (with the Laplace-Beltrami operator Delta) cannot. This is due to the fact that (under a natural compactness hypothesis), the Laplace-Beltrami operator is essentially self-adjoint on a connected component of the manifold without the singular set. In the literature such phenomenon is called quantum confinement.
In this talk we study the self-adjointness of the curvature Laplacian, namely −Delta+c K, for c>0 (here K is the Gaussian curvature), which originates in coordinate free quantization procedures (as for instance in path-integral or covariant Weyl quantization). We prove that there is no quantum confinement for these types of operators.

Homepage: http://www.cmapx.polytechnique.fr/~boscain/

Short biography

After the PhD in SISSA in 2000, and a post doc in France, he was hired as permanent researcher in SISSA in 2002. In 2006 he joined the CNRS in France: first in Dijon, then at Ecole Polytechnique (Palaiseau) and finally at LJLL Sorbonne Université, where he is director of Research.

He is member of the Inria Team CAGE and Professor "chargé de cours" of automatic control at Ecole Polytechnique.

His domain of research includes: geometric control, sub-Riemannian geometry, control of quantum mechanical systems.

He is an ERC StG laureate 2009 and ERC POC laureate 2016.

He wrote 2 books, more than 70 papers and supervised 10 PhD students.

Abstract: The problem of synthesizing a metabolite of interest in continuous bioreactors through resource allocation control is addressed. The approach is based on a self-replicator dynamical model that accounts for microbial culture growth inside the bioreactor, and incorporates a synthetic growth switch that allows to externally modify the RNA polymerase concentration of the bacterial population. The optimal control problem exhibits two ubiquitous phenomena: Fuller and turnpike.

Joint work with J.-L. Gouzé and A. Yabo (Sophia)

Homepage: http://caillau.perso.math.cnrs.fr/

Short biography

Jean-Baptiste Caillau is Professor of applied mathematics at Université Côte d’Azur, member of the CNRS lab J. A. Dieudonné in Nice, and of the McTAO team at Inria Sophia. He obtained his PhD in 2000 and has held positions in Toulouse and Dijon. He is interested by geometric and computational aspects of optimal control of dynamical systems.

Abstract: Analysis of population dynamics and changes in these dynamics under anthropogenic impact, for example, changes in the parameters of its habitat or exploitation of the population itself in any form, are in the focus of investigation of various research. In recent decades, the tasks of rational nature management, preservation of the environment and biodiversity have increased the demand for results in this area and increased the attention of scientists to this topic.

We consider an exploited population distributed in a periodic environment with independent point wise dynamics like the Verhulst model or with the same dynamics taking into account diffusion, which is already described by an equation of the Kolmogorov-Piskunov-Petrovsky-Fisher type. Under natural asumptions on the model parameters and average time quality criteria that characterize income from the exploitation in the long term, there is proved the existence of an optimal strategy of exploitation. (more ...)

Homepage: http://fpmf.vlsu.ru/index.php?id=419

Short biography

Alexey Davydov, Professor of the Moscow State University and of the National University of Science and Technology MISIS, Dr. Sc. Phys. Math. (Habilitation). He is an author of 2 books and numerous research papers. His main results pertain to the qualitative theory of differential equation and control systems, optimal control, and parametric optimization. He was awarded the Moscow Mathematical Society Prize (1986) and Maik Nauka-Interperiodica Award (2002). A. Davydov is a Member of the Editorial Boards of 2 journals. Under his scientific direction 8 PhD-theses were written and 3 are in preparation. He was Keynote Speaker and Invited Speaker, as well as a member of Program Committees, at various International conferences. A. Davydov is a Member of the Expert Council of the Russian Academy of Sciences, a Member of the Scientific Council of the Banach Center (Poland).

Abstract: In some cases, it is possible to construct Lévy-like processes where actions by random elements of a given semigroup play the role of increments. I discuss some cases where such construction is possible and cases where it can be shown to be impossible. The different outcomes are related to spectral properties of differential operators.

Homepage: https://www.iseg.ulisboa.pt/aquila/homepage/mguerra

Short biography

Manuel Guerra received a PhD in Mathematics at the University of Aveiro, in 2001, under the supervision of Andrey Sarychev.

He is Associate Professor at the Department of Mathematics at ISEG-Universidade de Lisboa, and a member of the research consortium CEMAPRE-REM.

His research interests lie in the fields of control theory, functional analysis, and stochastic processes. His published research includes both purely mathematical papers, and applications in the fields of actuarial science, mathematical finance, and economic modelling.

Abstract: This talk, based on joint work with Velimir Jurdjevic and Irina Markina, deals with sub-Riemannian structures associated with homogeneous spaces M= G/K induced by a transitive left action of a semi-simple Lie group G on a smooth manifold M, where K is the isotropy subgroup relative to a fixed point in M. A large class of sub-Riemannian systems on Lie groups that admit explicit solutions with certain important properties will be uncovered. The relevance of these results to the action of Lie groups on Stiefel and Grassmann manifolds will be emphasized.

Homepage: www.mat.uc.pt/~fleite/

Short biography

Fátima Silva Leite is a Full Professor (Emeritus since 17 March 2020) at the Department of Mathematics of the University of Coimbra and an active researcher at the Institute of Systems and Robotics, Coimbra. She obtained a PhD degree in Control Theory from the University of Warwick in 1982 and has been, since then, a Professor at the University of Coimbra, having obtained Habilitation in Mathematics from that university in 2003. Her main research interests lie in geometric nonlinear control and applications of differential geometry to solve problems in robotics and computer vision.

Fátima Silva Leite supervised 23 MSc students, 8 PhD students and 8 post-doc projects. She coordinated several national and international research networks and is an author of more than 110 research papers in Journals, Chapters of Books and Proceedings of International Conferences.

Abstract: This talk focuses on joint work with Maria Margarida A. Ferreira and Gueorgui Smirnov on optimal control problems involving sweeping processes. Here the sweeping system is defined as the 0 level set of twice continuously differentiable function. A remarkable feature of such problems is that the set valued function defining the dynamics fails to be Lipschitz. We derive results asserting the existence of solution as well as new necessary conditions using an ingenious sequence of approximating problems. We cover both problems with and without end state constraints. Exploring the nature of the approximating problems, we also produce numerical methods for these optimal control problems.

Homepage: https://paginas.fe.up.pt/~mrpinho/

Short biography

Maria do Rosário do Pinho is associated professor of the Department of Electrical and Computer Engineering of the University of Porto. Her research area is theory and applications of optimal control problems for ODEs, optimality conditions for constrained optimal control problems, free time problem, reachability sets and nonsmooth analysis., and applications of dynamic models in biomedicine, optimal control of UAV.

Maria do Rosário do Pinho is the author of one book and 3 book chapters, the author and co-author of more than 20 articles in peer-reviewed international journals. She supervised two PhD students and participated in eight national and international research projects.

Abstract: This talk focuses on sufficient second order conditions for strong local optimality of Pontryagin extremals in optimal control problems with a control affine dynamics and bounded controls.

If the cost is smooth, then the typical structure of extremal trajectories is the concatenation of bang and singular arcs.

We review some results for these kind of concatenations, obtained in collaboration with Gianna Stefani, and then consider the case of a Bolza problem, studied in collaboration with Francesca Carlotta Chittaro, where the integral cost has a $L^1$-growth with respect to the control. Indeed, with such a cost, extremals trajectories present also a new kind of arcs, which in the literature are known as "zero arcs" or "inactivated arcs".

Homepage: https://www.unifi.it/p-doc2-2017-200006-P-3f2a3d31362b2c-0.html

Short biography

After getting her PhD with a thesis on lower semicontinuity and implicit PDEs in the Calculus of Variations, Laura Poggiolini joined the Department of Applied Mathematics of the University of Florence and, under the supervision of Prof. Gianna Stefani, her research focused on the study of second order sufficient conditions in Optimal Control Problem via Hamiltonian methods. The research focuses in problems with a control-affine dynamics and due to them she also became interested in local inversion of piecewise-C¹ maps. She is currently with the Department of Mathematics and Information Sciences of the University of Florence.

Abstract: We consider the left-invariant sub-Riemannian structure on the free nilpotent Lie group of rank 2 and step 4, this structure has growth vector (2,3,5,8). We describe abnormal trajectories and study the abnormal set, i.e., the set of points filled by abnormal trajectories starting at the identity. In particular, we show that this set is sub-analytic of dimension 5. Moreover, this set is not closed, not smooth, and not semi-analytic. We discuss optimality of abnormal trajectories. Finally, we present some open questions.

Homepage: http://control.botik.ru/?staff=sachkov&lang=en

Short biography

Yuri L. Sachkov graduated from Lomonosov Moscow University (Department of Mathematics and Mechanics) in 1986. He defended a thesis of Candidate of Sciences “Controllability of 3-dimensional bilinear systems” in 1991 under leadership of Prof. Alexey F. Filippov in Moscow University. In 2008 Yuri Sachkov defended a thesis of Doctor of Sciences “Controllability and optimal control of invariant systems on Lie groups” in Steklov Mathematical Institute.

Yuri Sachkov is a co-author of the book “Control theory from the geometric viewpoint”, Springer, 2004, with Andrei A.Agrachev, and an author of the book “Controllability and symmetries of invariant systems on Lie groups and homogeneous spaces” (in Russian), Fizmatlit, 2007.

He is an author of more than 60 research papers in international and Russian journals on geometric control theory, sub-Riemannian geometry, and invariant systems on Lie groups and homogeneous spaces.

Abstract: By “elementary”, I do not mean Euclidean, axiomatic, high school geometry, nor do I mean that these results are expected or easy to obtain: I use this term to distinguish this subject from differential geometry. I have a collection of recent results that fall into this category, and I shall present a sampler; in most cases, these results were discovered in computer experiments and were motivated by the theory of completely integrable systems. The topics will include the circumcenter of mass of polygons, a new take on Steiner’s porism, new projective configuration theorems, and lesser known geometrical properties of Poncelet polygons.

Homepage: http://www.personal.psu.edu/sot2/

Short biography

Sergei Tabachnikov received PhD degree in mathematics from Moscow State University (1987). Until 1990, he was involved in several educational projects in the Soviet Union: taught at Gelfand’s School (Mathematics School by correspondence at Moscow State University) in 1979-88, and served as the head of mathematics department of “Kvant” magazine in 1988-90. Since 1990, he has taught at American Universities (first, University of Arkansas, later, at Penn State). At Penn State, he served as Director of MASS (Mathematics Advanced Study Semesters) program. In 2013-15, he served as Deputy Director of ICERM (Institute for Computational and Experimental Research in Mathematics) at Brown University. He is a Fellow of American Mathematical Society (inaugural class of 2012) and he served on various AMS committees. Sergei has served, or is serving, on various advisory and editorial boards. In particular, in 2013-19, he served as Editor-in-Chief of “Experimental Mathematics”, and he is an associate editor of “The American Mathematical Monthly", "The Mathematical Intelligencer”, and “Arnold Mathematical Journal”. He was a co-organizer of International Mathematical Summer School for Students and Chair of its Scientific Committee (2010–2017). Sergei is involved in various outreach activities, including mathematical circles in local elementary, middle, and high schools. Sergei's mathematical interests include differential geometry, differential topology, and dynamical systems, in particular, billiard models. His recent work focused on geometrical approaches to completely integrable systems, continuous and discrete. He authored two books on mathematical billiards, a book on modern projective differential geometry (jointly with V. Ovsienko), and "Mathematical Omnibus" (jointly with D. Fuchs), and expository book, translated into Russian, German, and Japanese.