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18402
01/02/2019

Hybrid models of opinion dynamics with opinion-dependent connectivity

P.FRASCA, S.TARBOURIECH, L.ZACCARIAN

GIPSA-Lab, MAC

Revue Scientifique : Automatica, Vol.100, pp.153-161, Février 2019 , N° 18402

Lien : https://hal.archives-ouvertes.fr/hal-01940187

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Abstract

This paper is a first attempt at using tools from the theory of hybrid systems to study opinion dynamics on networks with opinion-dependent connectivity. According to the hybrid framework, our dynamics are represented by the combination of continuous flow dynamics and discrete jump dynamics. The flow embodies the attractive forces between the agents and is defined by an ordinary differential equation whose right-hand side is a Laplacian, whereas the jumps describe the activation or deactivation of the pairwise interactions between agents. We first reformulate the classical Hegselmann–Krause model in this framework and then define a novel interaction model, which has the property of being scale-invariant. We study the stability and convergence properties of both models by a Lyapunov analysis, showing convergence and clusterization of opinions.

145456
18383
01/01/2019

Distributed estimation based on multi-hop subspace decomposition

A.RODRIGUES DEL NOZAL, P.MILLAN GATA, L.ORIHUELA, A.SEURET, L.ZACCARIAN

Loyola Andalucía, MAC

Revue Scientifique : Automatica, Vol.99, pp.213-220, Janvier 2019 , N° 18383

Lien : https://hal.laas.fr/hal-01920417

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This paper deals with the problem of distributedly estimating the state of an LTI plant through an interconnected network of agents. The proposed approach results in an observer structure that incorporates consensus among the agents and that can be distributedly designed, achieving a robust solution with a good estimation performance. The developed solution is based on an iterative decomposition of the plant in the local observable staircase forms. The proposed observer has several positive features compared to recent results in the literature, which include milder assumptions on the network connectivity and the ability to set the convergence rate.

145283
16375
01/01/2019

SPECTRA -a Maple library for solving linear matrix inequalities in exact arithmetic

D.HENRION, S.NALDI, M.SAFEY EL DIN

MAC, LIP6-CNRS, TU Dortmund

Revue Scientifique : Optimization Methods and Software, Vol.34, N°1, Janvier 2019 , N° 16375

Lien : https://hal.laas.fr/hal-01393022

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This document briefly describes our freely distributed Maple library spectra, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required.

146376
18387
01/01/2019

Detectability and observer design for switched differential–algebraic equations

A.TANWANI, S.TRENN

MAC, University of Groningen

Revue Scientifique : Automatica, Vol.99, pp.289-300, Janvier 2019 , N° 18387

Lien : https://hal.laas.fr/hal-01933110

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This paper studies detectability for switched linear differential–algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic stability of zero-output-constrained state trajectories, and building on our work on interval-wise observability, we propose the notion of interval-wise detectability: If the output of the system is constrained to be identically zero over an interval, then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval. Conditions are provided under which the interval-wise detectability leads to asymptotic stability of zero-output-constrained state trajectories. An application is demonstrated in designing state estimators. Decomposing the state into observable and unobservable components, we show that if the observable component of the system is reset appropriately and persistently, then the estimation error converges to zero asymptotically under the interval-wise detectability assumption.

145295
17247
01/01/2019

Stability analysis of a system coupled to a heat equation

L.BAUDOUIN, A.SEURET, F.GOUAISBAUT

MAC

Revue Scientifique : Automatica, Vol.99, pp.195-202, Janvier 2019 , N° 17247

Lien : https://hal.archives-ouvertes.fr/hal-01566455

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As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov functional technique. Inspired from recent developments in the area of time delay systems, a new methodology to study the stability of such a class of distributed parameter systems is presented here. The idea is to use a polynomial approximation of the infinite dimensional state of the heat equation in order to build an enriched energy functional. A well known efficient integral inequality (Bessel inequality) will allow to obtain stability conditions expressed in terms of linear matrix inequalities. We will eventually test our approach on academic examples in order to illustrate the efficiency of our theoretical results.

145732
17044
01/01/2019

D-optimal design for multivariate polynomial regression via the Chrstoffel function and semidefinite relaxations

Y.DE CASTRO, F.GAMBOA, D.HENRION, R.HESS, J.B.LASSERRE

LM, Orsay, IMT, Toulouse, MAC

Revue Scientifique : Annals of Statistics, Vol.47, N°1, pp.127-155, Janvier 2019 , N° 17044

Lien : https://hal.laas.fr/hal-01483490

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Abstract

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.

145392
18428
21/12/2018

Error analysis of some operations involved in the Fast Fourier Transform

N.BRISEBARRE, M.M.JOLDES, J.M.MULLER, A.M.NANES, J.PICOT

LIP, Lyon, MAC, ENS Lyon, UTCLUJ

Rapport LAAS N°18428, Décembre 2018, 32p.

Lien : https://hal.archives-ouvertes.fr/hal-01949458

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We are interested in obtaining error bounds for the classical FFT algorithm in floating-point arithmetic, for the 2-norm as well as for the infinity norm. For that purpose we also give some results on the relative error of the complex multiplication by a root of unity, and on the largest value that can take the real or imaginary part of one term of the FFT of a vector x, assuming that all terms of x have real and imaginary parts less than some value b.

145731
18451
19/12/2018

Observability of Discrete-Time Linear Systems with Communication Protocols and Dropouts

A.TANWANI, R.JUNGERS, W.P.M.H.HEEMELS

MAC, UCL, Eindhoven

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18451

Lien : https://hal.laas.fr/hal-01951815

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We consider the problem of analyzing observability in discrete-time linear systems when the sensors, deployed in a distributed manner, may not communicate to an observer at once, and a protocol determines the communication pattern among different sensors. We use the formalism of automata to model the sequence of measurements determined by a protocol and show that the question of observability is decidable for the resulting system. We give upper bounds on the number of measurements required for deciding observability. In addition, we consider the effects of dropouts, which may occur in communicating the measurements across the channel. Again using the formalism of automatons to model certain classes of dropouts combined with the protocol, it is shown that observability is decidable in finite time for measurements sent across a communication channel using a protocol, and subject to dropouts.

145899
18454
19/12/2018

Max-Min Lyapunov Functions for Switching Differential Inclusions

M.DELLA ROSSA, A.TANWANI, L.ZACCARIAN

MAC

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018 , N° 18454

Lien : https://hal.archives-ouvertes.fr/hal-01951377

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We use a class of locally Lipschitz continuous Lyapunov functions to establish stability for a class of differential inclusions where the set-valued map on the right-hand-side comprises the convex hull of a finite number of vector fields. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family of functions is a Lyapunov function for the system under consideration. For the case of linear systems, using the S-Procedure, our conditions result in bilinear matrix inequalities. The proposed construction also provides nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.

145905
18509
19/12/2018

Stability of distributed delay system with infinite support

Y.ARIBA, F.GOUAISBAUT, A.SEURET, K.LIU

MAC, CPPM

Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 6p. , N° 18509

Lien : https://hal.laas.fr/hal-01962563

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This paper is devoted to the stability analysis of infinite distributed delay systems. The basic idea is to model the original time-delay system into an interconnected feedback system in order to use robust analysis and especially quadratic separation. This approach has been widely used to study classical pointwise time-delay system. The stability analysis is performed by introducing new quadratic inequalities based on Laguerre polynomials particularly well fitted to deal with infinite distributed delay. It allows to develop new stability results which accuracy depends on the chosen polynomial degree.

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