1062documents trouvés
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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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.
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.
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.
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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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.
Exponential Lyapunov Stability Analysis of a Drilling Mechanism
M.BARREAU, A.SEURET, F.GOUAISBAUT
MAC
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° 18061
Lien : https://hal.laas.fr/hal-01725416
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This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.
Stabilization of an unstable wave equation using an infinite dimensional dynamic controller
M.BARREAU, F.GOUAISBAUT, A.SEURET
MAC
Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami Beach (USA), Décembre 2018, 7p. , N° 18221
Lien : https://hal.laas.fr/hal-01845845
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This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an infinite dimensional control law is therefore proposed to exponentially stabilize the system. The idea behind the choice of the controller is to extend the domain of the PDE so that the anti-damping term is compensated by a damping at the other boundary condition. Additionally, notice that the system can then be exponentially stabilized with a chosen decay-rate and is robust to uncertainties on the wave speed and the anti-damped coefficient of the wave equation, with the only use of a point-wise boundary measurement. The efficiency of this new control strategy is then compared to the backstepping approach.
Nonlinear control for an uncertain electromagnetic actuator
F.DESCHAUX, F.GOUAISBAUT, Y.ARIBA
MAC
Manifestation avec acte : IEEE Conference on Decision and Control ( CDC ) 2018 du 17 décembre au 19 décembre 2018, Miami (USA), Décembre 2018, 6p. , N° 18296
Lien : https://hal.laas.fr/hal-01868623
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This paper presents the design of a nonlinear control law for a typical electromagnetic actuator system. Electromagnetic actuators are widely implemented in industrial applications, and especially as linear positioning system. In this work, we aim at taking into account a magnetic phenomenon that is usually neglected: flux fringing. This issue is addressed with an uncertain modeling approach. The proposed control law consists of two steps, a backstepping control regulates the mechanical part and a sliding mode approach controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the presented approach.
Maximal Positive Invariant Set Determination for Transient Stability Assessment in Power Systems
A.OUSTRY, C.CARDOZO, P.PANCIATICI, D.HENRION
LIX, RTE, MAC
Rapport LAAS N°18377, Novembre 2018, 6p.
Lien : https://hal.archives-ouvertes.fr/hal-01923135
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This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is formulated as a semi-definitive program based on occupation measures and Lasserre's relaxation. An extension of the proposed method into a robust formulation allows us to handle Taylor approximation errors for non-polynomial systems. Results show the potential of this approach to limit the use of extensive time domain simulations provided that scalability issues are addressed.
An overview of recent advances in stability of linear systems with time-varying delays
Q.L.HAN, X.M.ZHANG, A.SEURET, F.GOUAISBAUT, Y.HE
Swinburne, MAC
Revue Scientifique : IET Control Theory & Applications, 15p., Novembre 2018, doi 10.1049/iet-cta.2018.5188 , N° 18362
Lien : https://hal.laas.fr/hal-01920425
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This paper provides an overview and in-depth analysis of rec ent advances in stability of linear systems with time-varyi ng delays. First, recent developments of a delay convex analys is approach, a reciprocally convex approach and the constru ction of Lyapunov-Krasovskii functionals are reviewed insightful ly. Second, in-depth analysis of the Bessel-Legendre inequ ality and some affine integral inequalities is made, and recent stability r esults are also summarized, including stability criteria f or three cases of a time-varying delay, where information on the bounds of the t ime-varying delay and its derivative is totally known, part ly known and completely unknown, respectively. Third, a number of stabi lity criteria are developed for the above three cases of the t ime-varying delay by employing canonical Bessel-Legendre inequalitie s, together with augmented Lyapunov-Krasovskii functiona ls. It is shown through numerical examples that these stability criteria o utperform some existing results. Finally, several challen ging issues are pointed out to direct the near future research.
Formal verification of an interior point algorithm instanciation
G.DAVY, E.FERON, P-L.GAROCHE, D.HENRION
ONERA, Georgia Institute, MAC
Manifestation avec acte : International Conference on Logic for Programming Artificial Intelligence and Reasoning ( LPAR ) 2018 du 16 novembre au 21 novembre 2018, Awassa (Ethiopie), Novembre 2018, 17p. , N° 18009
Lien : https://hal.archives-ouvertes.fr/hal-01681134
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With the increasing power of computers, real-time algorithms tends to become more complex and therefore require better guarantees of safety. Among algorithms sustaining autonomous embedded systems, model predictive control (MPC) is now used to compute online trajec-tories, for example in the SpaceX rocket landing. The core components of these algorithms, such as the convex optimization function, will then have to be certified at some point. This paper focuses specifically on that problem and presents a method to formally prove a primal linear programming implementation. We explain how to write and annotate the code with Hoare triples in a way that eases their automatic proof. The proof process itself is performed with the WP-plugin of Frama-C and only relies on SMT solvers. Combined with a framework producing all together both the embedded code and its annotations, this work would permit to certify advanced autonomous functions relying on online optimization.