All Years Seminars
[INMA] 2016-05-20 (15:00) : Differentially positive systems: asymptotic behavior and converse results
At Euler building (A002)
Speaker :
Fulvio Forni (University of Cambridge (UK))
Abstract :
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The novel notion of differential positivity extends linear positivity to the nonlinear setting: a nonlinear system is differentially positive if its linearization along trajectories leaves a cone (field) invariant. Notably monotone systems are differentially positive. Differential positivity extends monotonicity to manifolds, replacing order relations with local orders. The property strongly restricts the asymptotic nonlinear behavior, through suitable extensions of Perron-Frobenius theory and of results on contraction of the Hilbert metric. Motivated by the importance of positivity in linear systems theory, we discuss both the relevance of the property for applications and how much the property restricts the behavior of a nonlinear system.
[INMA] 2016-05-10 (14:00) : Gossip Coverage Control for Robotic Networks: Dynamical Systems on the Space of Partitions
At Euler building (A002)
Speaker :
Carli, Ruggero
Abstract :
Future applications in environmental monitoring, delivery of
services and transportation of goods motivate the study of deployment
and partitioning tasks for groups of autonomous mobile agents. These
tasks are achieved by recent coverage algorithms, based upon the
classic methods by Lloyd. These algorithms however rely upon critical
requirements on the communication network: information is exchanged
synchronously among all agents and long-range communication is
sometimes required. In this talk we discusses novel coverage
algorithms that require only gossip communication, i.e., asynchronous,
pairwise, and possibly unreliable communication. Which robot pair
communicates at any given time may be selected deterministically or
randomly. A key innovative idea is describing coverage algorithms for
robot deployment and environment partitioning as dynamical systems on
a space of partitions. In other words, we study the evolution of the
regions assigned to each agent rather than the evolution of the
agents positions. The proposed gossip algorithms are shown to
converge to centroidal Voronoi partitions under mild technical
conditions. Our treatment features a broad variety of results in
topology, analysis and geometry. First, we establish the compactness
of a suitable space of partitions with respect to the symmetric
difference metric. Second, with respect to this metric, we establish
the continuity of various geometric maps, including the Voronoi
diagram as a function of its generators, the location of a centroid as
a function of a set, and the widely-known multicenter function studied
in facility location problems. Third, we prove two convergence
theorems for dynamical systems on metric spaces described by
deterministic and stochastic switches.
We conclude the talk by proposing possible extensions of this novel
approach to other communication protocols, like asynchronous gossip
and asynchronous broadcast. A short discussion is devoted also to the
case where the multicenter function dictating the coverage is unknown
and possibly time-varying; in this scenario we combine the coverage
algorithms to estimation procedures which pair Gaussian processes
regression with Kalman filtering techniques.
[INMA] 2016-05-03 (14:00) : On some block diagonal preconditioners using spectral information to accelerate the solution of large linear systems
At Euler building (A002)
Speaker :
Charlotte Tannier (UNamur, Naxys)
Abstract :
Optimization problems with constraints arise in many areas of the sciences and engineering. In this context, the (possibly very large) linear systems which need to be solved in sequence have a saddle-point (or KKT) form. These systems are generally symmetric and indefinite, such that standard Krylov subspace methods like MINRES are applicable.
To accelerate the convergence of such iterative schemes, preconditioning techniques are usually considered, that improve the condition number and/or the eigenvalues clustering of the underlying matrices.
In this talk, we consider the « ideal » block diagonal preconditioner proposed by Murphy, Golub and Wathen (2000) and based on the exact Schur complement, and focus on the case where the (1,1) block has few
very small eigenvalues. Assuming that a good approximation of these eigenvalues and their associated eigenvectors is available, we propose different approximations of the block diagonal preconditioner of Murphy, Golub and Wathen, analyze the spectral properties of the
preconditioned matrices. We extend the previous approach for symmetric quasi-definite systems and we illustrate the performance of the proposed preconditioners through some numerical illustrations including the Stokes problem.
[INMA] 2016-04-26 (14:00) : Max-plus approximation of LU factorization
At Euler building (A002)
Speaker :
Françoise Tisseur (University of Manchester )
Abstract :
We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix $A$. Our method also predicts which
permutation matrices will be chosen by Gaussian elimination with partial pivoting or complete pivoting .It uses max-plus algebra and is based purely on the moduli
of the entries in the matrix. This approximation can be used in the construction of incomplete LU preconditioners as a mean to to quickly determine the positions of the largest
entries in the LU factors. These positions can subsequently be used as the sparsity pattern for an ILU preconditioner. This is joint work with James Hook.
[INMA] 2016-04-22 (11:00) : The Future Electric Power System-Developments and New Analysis Tools
At Euler building (A002)
Speaker :
Göran Andersson ( Power System Laboratory, ETH Zürich)
Abstract :
An effective and sustainable energy system is a fundamental prerequisite for the development of the society. In many parts of the world, the electric power system has over the last 100 years
developed to be the backbone of the energy system. Due to a number of new requirements, i.e. environmental, political, and economical, the electric power system is today facing a number of challenges
and problems, whose solutions require joint efforts from engineers, environmental scientists, economists, social scientists, etc. There are many indications that the future power and energy systems
will be more diverse as compared with the ones of today and yesterday. Non-dispatchable generators, energy storage, and consumers with load management schemes are examples of new system components.
Further, the electric power system will interact more with other energy carrier systems, such as gas and heating systems, and with other infrastructure systems such as transportation systems,
e.g. electric vehicles of different types.This lecture will give an overview and background of these challenges and current developments, particularly in Europe.
The above changes imply that the traditional ways of operating and planning the power systems are not always appropriate and new models and analysis tools are needed. In order to meet these new
modelling demands novel concepts for system-level considerations have been developed, which concepts allows the modelling of technologically diverse unit portfolios in a unified approach, e.g. the
energy hub and the power node approaches. These frameworks are used for designing operational strategies, especially in the presence of non-dispatchable generation and significant storage capacities,
as well as for evaluation of operational performance in terms of energy efficiency, reliability, environmental impact, and cost. This lecture will also discuss these models and tools, and their application
to system studies will be demonstrated.
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