All Years Seminars
[INMA] 2009-04-21 (14.00) : Optimization methods for sparse principal component analysis
At Euler building
Speaker :
Journée, Michel
Abstract :
Given an m-by-n matrix that stores m samples of n random variables, sparse principal component analysis (sparse PCA)
is the problem of finding a linear combination of these variables that is sparse ( i.e., that involves as few as possible of the original variables)
but that still captures as much as possible of the variance in the data. Sparsity is typically enforced for the sake of interpretability: components
that are linear combinations of a small number of the original variables are easier to interpret. Sparse PCA has applications in virtually all areas
of science, where large data sets need to be analyzed.
This talk is organized in two parts. First, we formulate sparse PCA as the maximization of a convex function on a compact set and propose a simple
gradient-method for this class of problems. We then consider convex relaxations of sparse PCA, which are optimization problems for positive semidefinite
matrices of potentially large dimension. For the sake of numerical efficiency, we discuss an approach that rests on low-rank positive semidefinite matrices,
which entail a quotient manifold structure.
[INMA] 2009-03-31 (14.00) : The Swarm-bot Experience in Swarm Robotics
At Euler building
Speaker :
Marco DORIGO (IRIDIA/ULB)
Abstract : A swarm-bot is an artifact composed of a swarm of assembled robots called s-bots.
The s-bots are mobile robots capable of connecting to, and disconnecting from,
other s-bots. S-bots have relatively simple sensors and motors and limited compu-
tational capabilities. In the swarm-bot form, the s-bots are attached to each
other, forming a single robotic system that can move and change its shape.
A swarm-bot can solve problems that cannot be solved by s-bots alone, and is par-
ticularly robust to malfunctioning components.
In the talk, after shortly describing the s-bots hardware and the
methodology we followed to develop algorithms for their control, I will focus on
the capabilities of the swarm-bot robotic system by showing video recordings of
some of the many experiments we performed to study coordinated movement, path
formation, self-assembly, collective transport, shape formation and
reconfiguration, distributed fault detection and other collective behaviors.
[INMA] 2009-03-24 (14.00) : LMI formulation for Optimal Control of coal fired Power Plants
At Euler building
Speaker :
Emile SIMON (CESAME)
Abstract :
Thermal power plants are usually controlled by classical regulations
(mostly PIDs), developed with a decentralised model, splitting the system
in many different SISO loops. However, multiple providers and distributed
generation are more likely to cause sudden and large changes of the load
demand. Improving the performance is thus a commercial commodity of great
importance in the current markets state of privatised power industry.
Therefore, we consider the solution of an optimal multivariable control.
The objective pursued here was already studied in a previous work
["Performance Limitations arising in the Control of Power Plants"
presented the 16/12/08 by Vincent Wertz], a key feature was the relation
between the value of the tracking cost and the delay structure of the
plant.
Here a new method is chosen, the problem is cast into an LMI formulation.
At first we develop the same trade-off results as previously found. But
now the new formulation allows one to add constraints with other LMI's.
Since in this paper the control energy is taken into account, a new LMI
reducing the control input is developed.
Without constraint, the coal flow input was too large. So a new LMI is
introduced, allowing to reduce the norm of the optimal controller and thus
the size of the input produced. This is shown to have a limited effect on
the original objective, meaning a slight impact on the performance.
We conclude from the results that the control is significantly improved,
while having control inputs within their limits.
[INMA] 2009-03-10 (14.00) : An LMI approach for uncertain nonlinear systems
At Euler building
Speaker :
Daniel COUTINHO (Pontifícia Universidade Católica do Rio Grande do Sul, Brazil.)
Abstract : In the last two decades, LMI-based techniques have been successfully applied to cope with uncertain linear
systems in a wide diversity of applications such as robustness analysis, control and filter design, H2 and H-infinity design,
control saturation and state-delayed systems. Together with the evolution of available LMI solvers, in terms of reliability,
computational burden and easily of coding, many researchers have developed different LMI methodologies to deal with
nonlinear systems. Recently, several different LMI-based techniques have been derived for nonlinear systems. One can
divide these works in two main classes: (i) the linear-like representations, and (ii) the SOS (sum of squares) approach.
The linear-like representations preserve the system state space representation and thus they can be applied for synthesis purposes.
However, global stability conditions are of difficult handling. In contrast, the SOS-based approaches may handle global stability
conditions but they are not suitable to control design. In this talk, the Differential-Algebraic Representation (DAR) framework is
introduced to deal with a large class of nonlinear systems. Some recent results on stability analysis, performance and control
synthesis are presented and a discussion is carried out on the advantages and shortcomings of the approach.
[INMA] 2009-03-03 (14.00) : New variants of nonnegative matrix factorization for sparsity improvement and maximum biclique finding
At Euler building
Speaker :
Gillis, Nicolas (UMons (Belgium))
Abstract : Nonnegative Matrix Factorization (NMF) is a data analysis technique which allows
compression and interpretation of nonnegative data. It has been extensively and successfully applied in numerous applications, e.g. text mining, spectral data
analysis, blind source separation, image processing, computational biology, graph clustering, recommendation systems, statistical models, etc. NMF consists in the
factorization of a nonnegative matrix by the product of two low-rank nonnegative matrices. Because of the nonnegativity constraints, NMF is particularly well-suited to achieve decomposition into parts.
In this talk, we first illustrate the usefulness of NMF with some application examples. We then present and analyze several algorithms to solve NMF.
In this study, we introduce two new variants of NMF: Nonnegative Factorization (NF) and Nonnegative Matrix Underapproximation (NMU). NF is a generalization of
NMF while NMU enables a recursive procedure for NMF and is particularly well-suited to achieve a better (sparser) part-based
decomposition. Algorithms and applications for both NF and NMU are presented.Finally, NF and NMU are shown to be NP-hard using a reduction to a graph partitioning problem, namely the maximum-edge biclique problem (MBP).
This reduction allows us design a new type of simple and efficient algorithm for MBP.
Seminars
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