All Years Seminars
[INMA] 2013-02-19 (14.00) : An introduction to the moment approach for optimal control
At Euler building
Speaker :
Mathieu Claeys
Abstract : This tutorial talk is devoted to the moment/sum-of-squares approach, which provides a general framework for global optimization of many
problems, including optimal control.
In the first part of the talk, we will review the philosophy of the approach on the problem of global minimization of a polynomial function, for
which the user-friendly GloptiPoly toolbox is readily available. The focus will therefore be on introducing the mathematical tools, such as measure
theory, and the elegant transformations that are used behind the scene by the software: transformation of the original problem into a linear problem
on measures, then manipulation of those measures by their moments to obtain tractable semi-definite relaxations.
The second part of the talk will show how to extend the approach for functional optimization problems such as optimal control. Measures arise quite
naturally in this context, and the moment approach is therefore well suited to tackle those problems fruitfully. This will be shown on the two examples
of bounded and impulsive control problems.
[INMA] 2013-02-12 (14.00) : Control of a reactor (to produce bioethanol) with discrete-delayed measurements
At Euler building
Speaker :
Hector Hernandez Escoto (Universidad de Guanajuato (Mexico))
Abstract : In this talk, the problem of controlling a continuous stirred tank fermenter of discrete-delayed measurements will be addressed.
The reactor is one to produce ethanol, and although this class of processes have been developed and industrially implemented since several
decades ago, the challenge of maintaining design conditions keeps, for ensuring production rates. In practical scenarios, these reactors
are operated on the basis of discrete-delayed measurements, provided by laboratory analysis of reacting mixture samples, taken out at certain instants.
Then, the design of a control system, following an input-output linearization approach, will be given taking in account the discrete-delayed
measurements; the design includes the following aspects: (i) characteristics of the dynamic behavior of the reactor, (ii) feasible control
configurations since instrumentation infrastructure, (iii) construction of control systems, (iv) a systematic scheme of tuning from a
pole-assignment approach, and (v) a discussion about the trade-off between sampling interval and convergence rate, since an analytical point of view
provided by a convergence analysis. Results will be illustrated with simulated cases, with a validated model of an industrial reactor.
[INMA] 2013-02-05 (14.00) : Mixing times on the cycle - can we decrease it?
At Euler building
Speaker :
Gerencser, Balazs
Abstract : We want to quickly generate a uniform random node of a graph using a Markov chain. The set of allowed transitions are given as the edges of
the graph but we can choose the transition probabilities. We start with the simple case of finding a quick reversible Markov chain on a cycle.
We then try to decrease the mixing time by different extensions: allowing non-reversible or time-inhomogeneous Markov chains or adding a small number of random edges to the cycle.
[INMA] 2013-01-24 (16.00) : Distorsion et trou spectral pour les graphes finis (MAPA Colloquium)
At Bât. Cyclotron, salle de convivialité math
Speaker :
Alain Valette (Université de Neufchâtel)
Abstract : Considérons un graphe fini X, qu'on voit comme espace métrique discret. La distorsion-$L^p$ de X est un invariant numérique qui mesure la difficulté à plonger $X$ isométriquement dans $L^p$. Un résultat fondamental de Bourgain (1984) dit que la distorsion-$L^p$ est bornée supérieurement par une fonction logarithmique du nombre de sommets du graphe.
Nous expliquerons une application de ce résultat à un problème algorithmique issu de linformatique théorique: MINCUT (trouver la coupure minimale dans un graphe).
Pour terminer, nous présenterons un résultat obtenu récemment avec P.-N. Jolissaint, qui donne une borne inférieure sur la distorsion dun graphe connexe fini, en terme du trou spectral,
c'est-à-dire de la première valeur propre du laplacien combinatoire du graphe. On en déduit une preuve très simple du résultat de Linial-London-Rabinovich (1995) que les graphes expanseurs se plongent dans $L^p$ avec distorsion logarithmique.
[INMA] 2012-12-11 (14.00) : On Reachability Analysis of Infinite-Dimensional Semilinear Systems
At Euler building
Speaker :
Elarbi Achhab (Université Cadi Ayyad and UCL)
Abstract : Many scientific and engineering problems can be modeled by partial differential equations that can be described as differential equations in infinite-dimensional spaces, using semigroups. An interesting example is given by the dynamics of (bio) chemical tubular reactors. In contrast to finite-dimensional linear systems, many different types of controllability and reachability may be defined for these control systems. The main ones are exact controllability, approximate controllability and regional controllability on a finite time interval [0, T], for which various equivalent conditions have been obtained in the literature. In the case of semilinear control systems, the study of reachability problems require some complicated and limited assumptions. The talk presents some results in this direction under assumptions which have a simple form and can be checked in many examples. The approach is developed using a state space systems framework and is based on the use of fixed-point theorems. The main idea is to transform the reachability problem into a fixed-point problem for an appropriate nonlinear operator in a function space. This will be illustrated by a significant example.
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