All Years Seminars
[INMA] 2010-11-09 (15.00) : Discontinuities and hysteresis in quantized average consensus
At Euler building
Speaker :
De Persis, Claudio
Abstract : We consider continuous-time average consensus dynamics,
discuss how quantization can be included in the system, and focus on
one model in which the agents'states are communicated through uniform
quantizers. We give a mathematical treatment in terms of differential
equations with discontinuous righthand side. Solutions to the
resulting system are defined in the Krasowskii sense, and results are
given proving their convergence to conditions of practical
consensus. In the case of symmetric graphs, these conditions
correspond to the equilibria of the system. To cope with potential
chattering phenomena, which may be undesired in the applications, we
propose the use of a hysteretic quantizer, and study the convergence
properties of the resulting dynamics by a hybrid system approach.
[INMA] 2010-11-02 (15.00) : Geometrical methods in observer design : observers and symmetries
At Euler building
Speaker :
Bonnabel, Silvère
Abstract : Observers compute a real-time estimation of the state of a dynamical
system from several sensor's (noisy) measurements. Most famous observers are the Luenberger observer and the Kalman filter,
both of them having been designed for
linear systems. For systems described by non-linear differential
equations, there is no general method to design observers. In this talk,
we propose to focus on a special class of nonlinear systems : systems
possessing symmetries (or invariances). For those systems we propose a
general method to build candidate observers which respect the
symmetries. For instance the conservation laws involved in the models of
chemical reactors are independent of the choice of physical units (mol,
kg, ...). In this case, the method allows to find all observers which
are also invariant to a change of units. We will apply the method to the
example of multisensor fusion for mobile vehicles, in which the
symmetries are the Galilean invariances.
The theory only deals with a limited number of symmetries (for instance
a change of physical units). At the end of the talk, we will also
consider the problem of designing a velocity observer for conservative
Lagrangian systems with configuration (position) measurements, invariant
to all possible change of coordinates (infinite number of symmetries).
We will use the Jacobi metric, and we will view the Lagrangian dynamics
of a conservative system as a geodesic flow on a manifold. This work is
based on the paper by Aghannan and Rouchon (IEEE-TAC, 2003).
[INMA] 2010-10-19 (15.00) : A new result on unconditional convergence in continuous-time consensus
At Euler building
Speaker :
Hendrickx, Julien
Abstract : We consider systems of n agents holding each a real value. This value is
continuously attracted by the values of some other agents according to
pre-determined or dynamical rules. These simple continuous-time
consensus-seeking systems are the basis on which is built several
decentralized control laws.
We give a new weak condition under which the convergence of the system
is guaranteed, and characterize the limiting points of the systems.
Unlike previous results on such systems, our condition is instantaneous:
It concerns the nature of the interactions at every time as opposed to
their evolution. This aspect is particularly important when treating
systems with state-dependent interactions, whose evolution is a priori
unknown. Moreover, our condition is weaker than all previously proposed
conditions for convergence.
We explore different possibilities of extension of our results to
similar consensus seeking systems and survey some particular cases. We
also show how our result helps analyzing systems to which no previous
generic result could be applied, with a particular focus on opinion
dynamics.
[INMA] 2010-10-12 (15.00) : Multigrid-based solvers for mixed partial differential equations
At Euler building
Speaker :
Samuel MELCHIOR (UCL)
Abstract : Solving efficiently the incompressible NavierStokes equations is a major
challenge, especially in the three-dimensional case. One interesting
approach consists in applying a preconditioned GMRES method to the
linearized problem at each iteration of a nonlinear scheme. The
preconditioner can be built as an approximation of an ideal
block-preconditioner that guarantees convergence in 2 or 3 iterations. In
this talk, we investigate the numerical behavior for the three-dimensional
lid-driven cavity problem with wedge elements; the ultimate motivation of
this analysis is indeed the development of a preconditioned Krylov solver
for stratified oceanic flows which can be efficiently tackled using such
meshes. Numerical results for steady-state solutions of both the Stokes
and NavierStokes problem are presented. Theoretical bounds on the
spectrum and the rate of convergence appear to be in agreement with the
numerical experiments. Sensitivity analysis on different aspects of the
structure of the preconditioner and the block decomposition strategies are
also discussed. Particular emphasis is put on how to use the multigrid
scheme in this preconditioner. Extensions to the two-dimensional shallow
water equations are discussed.
[INMA] 2010-10-05 (15.00) : Networked Control Systems: a Discrete-time Approach
At Euler building
Speaker :
Nathan VAN DE WOUW (Eindhoven University of Technology)
Abstract : Networked Control Systems (NCSs) are control systems in which the
controller communicates with the sensors and actuators of the plant over
a communication network (e.g. a wireless network).
The advantages of the exploitation of such communication networks in the
context of control are flexible architectures
and a reduction of installation and maintenance costs. Important
disadvantages of NCSs are network-induced effects such as delays,
variable sampling intervals, packet dropouts and communication
constraints. These network-induced effects may have a detrimental effect
on the stability and performance of the control system. In this
presentation, we therefore present results on the robust stability and
stabilisation of NCSs in the face of such network-induced effects. Here
we will focus on a discrete-time modelling approach for the description
of linear NCSs with these network phenomena. This discrete-time NCS
model is used to formulate sufficient conditions in terms of Linear
Matrix Inequalities for both the robust stability analysis and the
synthesis of stabilising controllers for linear NCS. Besides the
stabilisation problem, also results on the tracking of time-varying
reference trajectories in a networked setting are presented.
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