Control in Times of Crisis.
Online seminar.
This scientific activity is a continuation of the online seminar Control en Tiempos de Crisis, this time addressing the international community interested in mathematical problems from control of differential equations, inverse problems and related subjects.
The seminar will take place each tuesday at 10 AM in Mexico / 12: 00 AM in Chile / 5:00 PM in Berlin, Roma, Madrid, Paris in the platform Zoom. We plan to alternate talks of senior and junior researchers.
NB: Starting from January 2021, the seminar will be shifted to thursday at the same time.
The link of each talk will be sent to the mailing list of the seminar. In order to be included in the list, please send a message to one of the organizers.
| Date | Speaker | Title / Abstract | |
|---|---|---|---|
| September 8 | Jean-Michel Coron (U Pierre et Marie Curie, France) |
Rapid and finite-time stabilization.
We present various results on the rapid and the finite-time stabilization of control systems. This includes control systems in finite dimension (with an application to a quadcopter sliding on a plane) as well as control systems modeled by means of partial differential equations (1-D linear hyperbolic systems, 1-D linear parabolic equations and KdV equations). |
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| September 15 Talk 1 |
Claudia Moreno (Université Paris-Saclay (UVSQ)) |
Control of a partial differential equation system of dispersive type.
In this talk, we study the exact controllability of a system composed by N Korteweg-de Vries equations. This model is known in the litera- ture as the KdV equation on a finite star-shaped network which is used to model for instance the cardiovascular system. The system originally was controlled in the literature considering N Korteweg-de Vries equations and N + 1 controls : N controls at the ends of the network and one control in the center of the network. We prove that the system remains controllable without the control acting in the center of the network. Thus, we prove the exact controllability of the system with N controls. We use the duality and multiplier method to study the controllability of the linearized system around the origin and the result for the nonlinear system is obtained by applying a fixed-point argument. | |
| September 15 Talk 2 |
Irene Marin-Gayte (U Sevilla, Spain) |
Theoretical and numerical bi-objective optimal control: Nash equilibria.
This talk deals with the solution of some multi-objective optimal control problems for several PDEs: linear and semilinear elliptic equations and stationary Navier-Stokes systems. More precisely, we look for Nash equilibria associated to standard cost functionals. We deduce appropiate optimality sys- -tems and we present some iterative algorithms. For the existence and characterization of Nash equilibria in the Navier-Stokes case, we use the formalism of Dubovitskii and Milyutin. In this framework, we also present a finite element approximation of the bi-objective problem and we illustrate the techniques with several numerical experiments. |
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| September 22 | Marius Tucsnak (U Bordeaux, France) |
Does the boundary controlled heat equation define an exactly controllable system?
It is commonly accepted in the control theory of PDEs that parabolic equations, due to the smoothing effect, do not determine exactly controllable systems when controlled from the boundary. The aim of this presentation is to explain how the heat semigroup can be restricted to an appropriate function space on which, when controlled from the boundary, it could determine an exactly controllable systems. To this aim, we first recall some abstract concepts concerning reachability in an infinite dimensional context, insisting on the general relevance of the concept of reachable space. We next describe some recent advances on the reachable space of the boundary controlled heat equation in one space dimension. We next discuss the exact controllability of this system in appropriate spaces of analytic functions. We give applications in determining the reachable space with smooth inputs, with possible application to nonlinear problems. Finally, we discuss the possible implications of our methods to improve the existing estimates of the control constant in small time. Slides. |
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| September 29 Talk 1 |
José Antonio Villa (UNAM, Mexico) |
Hierarchical control for the semilinear heat equation.
Abstract: We present some results about hierarchical control of the semilinear heat equation where the follower control must steer the solution to zero in some positive time and the leader control must minimise a given functional. Also, results about the same objectives control problem are done for the case when the controls are both inner controls and boundary conditions. | |
| September 29 Talk 2 |
Gilcenio Rodrigues (U F di Piaui, Brazil) |
Boundary controllability of a one-dimensional phase-field system with one control force
Abstract. |
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| October 6 | Piermarco Cannarsa (U Roma 2, Italy) |
Bilinear control for evolution equations
Abstract: Bilinear control systems are receiving increasing attention as they can be used to study problems for which an additive control action is out of question. For such systems, in infinite dimension, weaker controllability properties can be expected than for additive controls. For instance, exact controllability is out of question due to a well-known negative result by Ball, Marsden, and Slemrod back in the 80ies. Nevertheless, one can seek to steer states to special targets either in finite or infinite time.In this talk, the above problem will be addressed for evolution equations of the form u'(t)=Au(t)+p(t)Bu(t) where A and B are linear operators in a Hilbert space and p(t) is a single-input control. Applications to parabolic equations in one space dimension will also be discussed. |
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| October 13 Talk 1 |
Amaury Hayat (Ecole des Ponts Paristech) |
Stabilization of some nonlinear hyperbolic PDEs
Abstract: We consider two types of systems : density-velocity systems and traffic flows. Density-velocity systems encompass many physical equations: isentropic Euler equations, Saint-Venant equations, osmosis model, etc. We show that these equations have a local dissipative property that allows to stabilize any steady-state with boundary feedback controls, provided some physical assumption. Moreover, this holds even if we have no knowledge of some the system parameters or with a single control. Traffic flows are very interesting from a control perspective. In many situations the steady-states are unstable, leading to travelling waves, known as stop-and-go waves by engineers or simply jam. From a mathematical point of view they can be represented by coupled hyperbolic PDEs with solutions of class BV. We will present on-going work showing how one can try to stabilize the steady-states using autonomous vehicles, i.e. pointwise controls. This leads to a system of ODEs and PDEs coupled by a flux relation, which provoke non-classical shocks. The solutions are then at most BV and the control is contained in the dynamics of the ODEs. |
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| October 13 Talk 2 |
Chenmin Sun (U. Cergy) |
Classical and semi-classical observability for the Bouendi-Grushin operator
Abstract: The observability for the classical Schrödinger equation usually holds for very short time, under suitable geometric conditions. However, it is not the case when the underlying geometry is sub-elliptic. In this talk we consider the Schrodinger equation associated with the Bouendi- Grushin operator. The Bouendi-Grushin operator is a subelliptic operator which is degenerate along a line. In the Bouendi case, the associated Schrödinger equation exhibits a transport effect which leads to a "sub-elliptic" geometric control condition and a minimal time to ensure the observability. For general Bouendi-Grushin with stronger sub-elliptic effect, the observability for the Schrödinger equation is never true. These observability results can be seen from a semi- classical point of view, through a optimal resolvent esti- mate. Consequently, our resolvent estimate leads to an energy decay rate for the associated damped wave equation. This talk is based on a joint work with Nicolas Burq and another with Cyril Letrouit. Slides. |
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| October 20 | Karl Kunisch (U Graz, Austria) |
Solution Concepts for Optimal Feedback Control of Nonlinear Partial Differential Equations
Abstract: Feedback control of nonlinear systems in practice is still frequently based on linearisation and subsequent treatment by efficient Riccati solvers. Here we want to follow different directions. I concentrate on three solution strategies which aim at the nonlinear control system directly. The first one is based on higher order Taylor expansions of the value function and leads to controls which rely on generalized Ljapunov equations. The second approach is based on Newton steps applied to the HJB equation. Combined with spectral techniques and tensor calculus this allows to solve HJB equations up to dimension 100. The results are demonstrated for the control of discretized Fokker Planck equations. The third technique circumvents the direct solution of the HJB equation. Rather a neural network is trained by means of a succinctly chosen ansatz and it is proven that it approximates the solution to the HJB equation as the dimension of the network is increased. This work relies on collaborations with T.Breiten, S.Dolgov, D.Kalise, L.Pfeiffer, and D.Walter. |
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| October 27 Talk 1 |
Yuri Thamsten (U. Fluminense, Brazil) |
Local null controllability of a class of non-Newtonian incompressible viscous fluids
Abstract. |
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| October 27 Talk 2 |
Jeffrey Park (U Alaska Fairbanks,US) |
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| November 3 | Belhassen Dehman (Fac. des Sciences de Tunis, Tunisia) |
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| November 10 Talk 1 |
Kevin Le Balc'h (U Bordeaux, France) |
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| November 10 Talk 2 |
Jon Asier Barcena-Petisco (U Autonoma Madrid, Spain) |
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| November 17 | Suzanne Lenhart (U. Tennessee, US) |
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| November 24 Talk 1 |
Cristina Urbani (GSSI, Italia) |
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| November 24 Talk 2 |
Wencel Valega Mackenzie (U. Tennessee Knoxville, US) |
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| December 1 | Ozkan Ozer (Western Kentucky U, US) |
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| December 8 Talk 1 |
Jorge Zavaleta (UNAM, Mexico) |
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| December 8 Talk 2 |
Lucas Machado |
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| December 15 | Julie Valein (U Lorraine, France) |
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| January 7 Talk 1 |
Kuntal Bhandari (U. Toulouse, France) |
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| January 7 Talk 2 |
Rogelio Ortigosa (Cartagena, Spain) |
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| January 14 | Nicolas Burq (U Paris Sud, France) |
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| January 21 Talk 1 |
Denilson Menezes (U.F. Fluminense, Brazil) |
On equilibria for generalized Boussinesq fluid-chemical models with multiplicative controls
Abstract: We investigate equilibria for multi-objective optimal control problems in a model of fluid-chemical interactions. The action of the controls occurs multiplicatively, a pertinent assumption for certain practical circumstances, e.g., the study of ocean pollution control. For a single agent, we provide a characterization of the Pareto front in terms of a suitable class of minimization problems, each of which being equivalent to solving an optimality system. In the multi-agent competitive setting, each agent seeks to minimize her performance criteria to attain Pareto optimality, and we investigate Nash equilibria in this context. We derive and analyze the resulting optimality system in the latter framework. |
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| January 21 Talk 2 |
Cristobal Merono (Madrid, Spain) |
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| January 28 | Irena Lasiecka (U Memphis, US) |
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| February 11 | Rafael Vazquez (U Sevilla, Spain) |