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Séminaire du département Automatique du 06/12/2013 à 14h00

 

Session spéciale doctorants

Intervenant : D. Tran, F. Ruggero, A. Castellanos, H. Shiromoto, T. Ying, , Gipsa-Lab

Lieu : Salle des séminairesdu DAUTO, B. 208, Gipsa-Lab, Bat B, 2ème étage

 

Résumé :

Résumés

 

A. Castellanos Silva: « Adaptive feedback compensation for active vibration control: methodology, 
applications and perspectives»

Adaptive feedback compensation has proven to be an important tool for the active vibration control field. When the disturbance is characterized as a narrow-band one, its improvements with respect to a feedforward approach includes lower complexity (number of parameters to adapt) and relatively low-cost (no additional transducer). Nevertheless, due to the Bode Integral effect over the Output Sensitivity Function, major challenges in performance and robustness arise. Furthermore, possible parameter variations (incertitude) play an important role in order to achieve the control objective and fulfill performance specifications. Considering a Youla-Kucera parametrization (Q-filter) for the controller, several improvements can be achieved. A new methodology for the central controller design was developed and real-time results obtained in the framework of an International Benchmark shows its efficiency. New research interest includes the modification of the instrumental variable used for the adaptation and the contributions of an IIR-filter realization for the Q-filter.


D. Tran: “Consensus-based Distributed Methods for graph Laplacian Spectrum Estimation

 Our work deals with consensus-based distributed methods for estimating eigenvalues of the Laplacian matrix associated with the graph describing the network topology of a multi-agent system. As recently shown, the average consensus matrix can be written as a product of Laplacian-based consensus matrices whose stepsizes are given by the inverse of the nonzero Laplacian eigenvalues. Therefore, by solving the factorization of the average consensus matrix, the Laplacian eigenvalues can be inferred. The problem is posed as a constrained consensus problem. The proposed algorithms allow estimating the Laplacian spectrum with high accuracy with low computation and storage complexity.  

 

R. Fabbiano: « Source localization by gradient estimation based on Poisson integral»

We consider the problem of localizing the source of a diffusion process. The source is supposed to be isotropic, and several sensors, equipped on a vehicle moving without position information, provide pointwise measures of the quantity being emitted. The solution we propose is based on computing the gradient — and higher-order derivatives such as the Hessian — from Poisson integrals: in opposition to other solutions previously proposed, this computation does neither require specific knowledge of the solution of the diffusion process, nor the use of probing signals, but only exploits properties of the PDE describing the diffusion process. The theoretical results are illustrated by simulations.

 

 H. Stein Shiromoto: « A Region-Dependent Gain Condition for Asymptotic Stability»

 A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the function resulting from the gains composition to be continuous, increasing and upper bounded by the identity function. In this work, it is presented an alternative sufficient condition when such criterion fails due to either lack of continuity or the bound of the composed gain is larger than the identity function. More precisely the local (resp. non-local) asymptotic stability of the origin (resp. global attractivity of a compact set) is ensured by a region-dependent small gain condition. Under an additional condition that implies the absence of limit sets in a suitable domain, the almost global asymptotic stability of the origin is ensured. An example illustrates and motivates this approach.

 

Y. Tang: “A new H2-norm Lyapunov function for the stability of a singularly perturbed system of two conservation laws

In this talk a class of singularly perturbed system of conservation laws is considered. More precisely a linear system of two conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system can be treated as two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H2-norm for a singularly perturbed system of conservation laws is constructed. It is based on the Lyapunov functions of two subsystems in L2-norm.

 

P.-O. Lamare: “Lyapunov techniques for stabilization of switched linear systems of conservation laws

In this paper, the exponential stability in $L2$-norm is investigated for a class of switched linear systems of conservation laws. The state equations and the boundary conditions are both subject to switching. We consider the problem of synthesizing stabilizing switching controllers. By means of Lyapunov techniques, three control strategies are developed based on steepest descent selection, possibly combined with a hysteresis and a low-pass filter. Some numerical examples are considered to illustrate our approach and to show the merits of the proposed strategies.


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