Control in Times of Crisis.
Online seminar.

NEWS Next talk, October 20: Karl Kunisch.

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.

All talks are available on our youtube channel. Last talk: Amaury Hayat and Chenmin Sun.

The information of this seminar is published in Researchseminars

Next talks:
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).
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.
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.
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

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.
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.
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.
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.
October 27
Talk 1
Yuri Thamsten
(U. Fluminense, Brazil)
Local null controllability of a class of non-Newtonian incompressible viscous fluids

October 27
Talk 2
Jeffrey Park
(U Alaska Fairbanks,US)
November 3 Belhassen Dehman
(Fac. des Sciences de Tunis, Tunisia)
November 10
Talk 1
Kevin Le Balc'h
(U Bordeaux, France)
November 10
Talk 2
Jon Asier Barcena-Petisco
(U Autonoma Madrid, Spain)
November 17 Suzanne Lenhart
(U. Tennessee, US)
November 24
Talk 1
Cristina Urbani
(GSSI, Italia)
November 24
Talk 2
Wencel Valega Mackenzie
(U. Tennessee Knoxville, US)
December 1 Ozkan Ozer
(Western Kentucky U, US)
December 8
Talk 1
Jorge Zavaleta
(UNAM, Mexico)
December 8
Talk 2
Lucas Machado
December 15 Julie Valein
(U Lorraine, France)
January 7
Talk 1
Kuntal Bhandari
(U. Toulouse, France)
January 7
Talk 2
Rogelio Ortigosa
(Cartagena, Spain)
January 14 Nicolas Burq
(U Paris Sud, France)
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.
January 21
Talk 2
Cristobal Merono
(Madrid, Spain)
January 28 Irena Lasiecka
(U Memphis, US)
February 11 Rafael Vazquez
(U Sevilla, Spain)

  • Next free slots:

  • Organizers:
    Luz de Teresa UNAM México / Universidade Federal da Paraíba, Brasil.
    Sylvain Ervedoza Université de Bordeaux / CNRS.
    Enrique Fernández Cara Universidad de Sevilla, España.
    Alberto Mercado Saucedo UTFSM, Valparaíso Chile.