All Years Seminars
[INMA] 2010-12-14 (15.00) : Diffusive representation and application to the analysis and the resolution of non local dynamic problems
At Euler building
Speaker :
Céline CASENAVE (UCLouvain)
Abstract : In lots of dynamic systems of Physics or others scientific fields such as Biology, dynamic integral operators, often of convolution type, are
involved. On the contrary of the standard case of differential models, problems relating to integro-differential models are often difficult to solve,
especially because these models are not time-local.
In this context, the methodology called "diffusive representation" presents some interests: an integral operator is represented by its γ-symbol,
directly deduced from its transfer function, and can be formulated by means of a state realisation whose dimension is numerically reasonable
whatever the size of the system may be. In addition to this interesting practical side, the diffusive representation offers a unified mathematical
framework, well adapted to analysis of integral convolution operators.
The first part of the talk will be an introduction to the diffusive representation, the principle and the main results of which will be given.
The second part will deal with some dynamic problems which can be tackled in an original and quite simple way by using the diffusive representation.
In fact, all the operatorial problems of modelisation, simulation, control, model identification, model reduction, etc. can be formulated in such a way
that the object of the problem is the γ-symbol of the operator solution.
[INMA] 2010-12-09 (16.30) : Colloquium CESAME-MAPA - Random matrix theory and stochastic geometry in compressed sensing
At Auditoire Ch.-J. de La Vallée Poussin (Cycl.01)
Speaker :
Jared TANNER (University of Edinburgh)
Abstract : Compressed sensing is a new paradigm in signal processing, showing that for signal which are compressible, one can directly make
compressible measurements of the optimal order in a simple linear way. The majority of the results in this field are proven by establishing
new results in random matrix theory and stochastic geometry. This new theory and its methods of analysis will be discussed.
[INMA] 2010-12-07 (15.00) : Applications of DEIM in Nonlinear Model Reduction
At Euler building
Speaker :
Dan SORENSEN (Rice University)
Abstract : A dimension reduction method called Discrete Empirical Interpolation (DEIM) is described and shown to dramatically reduce the
computational complexity of the popular Proper Orthogonal Decomposition (POD) method for constructing reduced-order models for parametrized nonlinear
partial differential equations (PDEs). DEIM is a technique for reducing the complexity of evaluating the reduced order nonlinear terms obtained with
the standard POD-Galerkin. POD reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear
term remains that of the original problem. DEIM is a modification of POD that reduces complexity of the nonlinear term of the reduced model to a cost
proportional to the number of reduced variables obtained by POD. The method applies to arbitrary systems of nonlinear ODEs, not just those arising
from discretization of PDEs.
In this talk, the DEIM method will be developed along with a discussion of its approximation properties. Applications from Neural Modeling,
Chemically Reacting Flow, Shape Optimization and Porous Media Flow will be presented to illustrate the effectiveness and wide applicability of
the DEIM approach.
[INMA] 2010-11-23 (15.00) : Why should a control theorist care about symbolic dynamics?
At Euler building
Speaker :
Jungers, Raphaël M.
Abstract : Symbolic dynamics is a beautiful theory, at the frontier between Mathematics, Computer science, Combinatorics (on words) and Graph Theory.
The basic objects of study in this theory are the so-called "shifts": these are sets of infinite words which are closed to translation. A priori,
no relation with the control of hybrid system... or does it?
We will see how symbolic dynamics and hybrid control are intimately related, by going back to the origin of this nice theory. This will enable us
to derive a large family of LMI conditions for the stability of hybrid systems, which actually encompasses many of the ones previously studied in the
literature. This provides new methods that appear very efficient in practice for the analysis and design of hybrid systems.
Joint work with A.A. Ahmadi, P. Parrilo, M. Roozbehani.
[INMA] 2010-11-16 (15.00) : Optimization & Control: Solving BMI problems via LMI coordinate descent
At Euler building
Speaker :
Emile SIMON (CESAME)
Abstract : In this talk we will discuss a method to solve Bilinear Matrix
Inequalities (BMIs), in particular in their original field of optimal
control. Starting from an initial solution, the idea used is to fix one
side of the BMIs and solve the resulting LMIs problem, then fix this new
side, free the other side of the BMIs, solve the new LMIs problem and
iterate between these two steps. This is in fact a coordinate descent
algorithm. The motivation is to reach a local optimum in polynomial time
(difficult because BMIs are in general non-convex and N-P hard). This
method is mostly overlooked because it is not guaranteed to reach the
global optimum but also not even local optimae in general. Indeed we will
see that the first algorithm proposed in the literature implementing this
technique, fixing either all of the Lyapunov matrix(ces) or the control
parameter of the optimal control problem (so-called V-K iteration), cannot
work and why.
The contributions of the current work are the following. First, the
problem and difficulties are outlined with a short survey of relevant
papers and useful results. Then, the use of a particular change of
variables (thus of coordinates) is made so that the algorithm will improve
the initial suboptimal solutions (for fixed-order output-feedback control
design for LTI systems). Finally, an important improvement is
proposed that probably ensures convergence towards local optimality.
Although the exact convergence conditions are still under investigation,
the algorithm (that could be interpreted as a BMI interior point method)
performs well in practice which will be shown by means of an example.
Seminars
Subscribe (ICS)
INMA Contact Info
Mathematical Engineering (INMA)
L4.05.01
Avenue Georges Lemaître, 4
+32 10 47 80 36
secretaire-inma@uclouvain.be
Mon – Fri 9:00A.M. – 5:00P.M.
JOIN US