Réunion GT SYNC et Observation (1)

Mardi 15/11 de 14h45 à 17h15

Programme

14h45-15h30:   Nicolas Petit 

CAS – Centre Automatique et Systèmes, MINES ParisTech

Titre: Angular velocity nonlinear observer from single vector measurements

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15h35-16h20:  Irene Sendiña-Nadal ^1,2

¹ Complex Systems Group - Universidad Rey Juan Carlos, Madrid, Spain

² Laboratory of Biological Networks, Center for Biomedical Technology,

Technical University of Madrid, Spain

Titre : Structure and synchronization dynamics in complex networks

Résumé: A complex network is an abstract representation of a complex system composed of many entities (neurons, proteins, computers, web pages, people ...) interacting among them in a non-random or regular way. In this talk, I will start overviewing some concepts from graph theory to characterize the topology of a complex network (clustering, shortest path, degree distribution ...) [1] and to apply them to analyze in vitro neuronal networks during their development. This longitudinal study of the evolution of the main topological observables points out to the existence of a particular state corresponding to a small-world network configuration [2], characterized by large values of the clustering (the presence of triangles) and small values of the average distance between any pair of nodes, with several implications in the functionality of the neuronal network.

 Then, I will consider a dynamical network whose nodes are nonlinear oscillators (periodic or chaotic) and I will highlight the importance of the coupling structure (random, scale-free...) to support synchronous states through a master stability function approach (MSF) [1]. This approach provides the necessary conditions for the synchronizability of the dynamical network where both the local function (describing the dynamics of a single oscillator) and the output function (describing the topology of the connectivity and the type of coupling variable) are combined in a function of a single normalized coupling parameter. As an application of the MSF, I will show how to steer (target) the network's dynamics towards a given, desired evolution performed here by a master network. By unidirectional coupling a specific set of nodes from the master network to their copies in the slave network, the driven network is able to pursue a goal dynamics compatible with the natural evolution of the system from the attractor basin [3].

 Finally, I will provide another example showing the impact of a given network architecture in the phase transition to synchronization. By introducing a functional dependence between the natural frequencies of the oscillators and their degrees (the number of neighbors a node has), an abrupt transition -of first-order like- to synchronization can be induced for sufficient heterogeneous degree distributions [4-6].

 [1] Boccaletti et al., Phys. Rep. 424, 175-308 (2006); Boccaletti et al., Phys. Rep. 544, 1-122 (2014)

 [2] D. de Santos-Sierra et al., PLOS ONE 9:e85828 (2014)

 [3] R. Gutierrez et al., Sci. Rep. 2: 396 (2012)

 [4] Leyva et al., Phys. Rev. Lett. 108, 168702 (2012); Sci. Rep. 3:1281 (2013); Phys. Rev. E 88, 042808 (2013)

 [5] I. Sendiña-Nadal et al., Phys. Rev. E 91, 032811 (2015)

 [6] Boccaletti et al., under review in Phys. Rep. (2016)

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16h25-17h10:  Christophe Letellier

CORIA – Université de Rouen

Titre : To be synchronizable or not…is it related to observability ?

Résumé: With the explosion of networks in modern life, determining whether oscillators can  synchronize or not has many practical applications in power grids, biological networks, epidemiology, social networks… In spite of this, although anyone intuitively understands what  synchronizability means, a non-ambiguous mathematical definition is still missing, not only because there are many types of synchronization (full, phase, frequency, generalized, intermittent …) but also because synchronizability depends on few components which have yet to be clarified. We will discuss what are the main ingredients required to determine a priori – from the set of governing equations – whether or not a given set of coupled oscillators can synchronize. The considered criteria  (phase, observability, dynamics) allow to rank the different variables used for describing the states of the oscillators by decreasing the degree of synchronizability (cases of the Rössler, Lorenz 63, Lorenz 84 and Hindmarsh-Rose  systems will be explicitly provided). We will also present how the synchronization between strongly dissipative systems can be assessed from the measurements in a single oscillator.

We will end this talk by explaining how symbolic observability coefficients can be used to assess the observability of complex systems and networks.

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Réunion GT SYNC et Observation (2)

Mercredi 16/11 de 9h15 à 11h45

Programme

9h15-10h00: Xing Wei,  Da-Yan Liu,  Driss Boutat

PRISME, INSA Centre Val de Loire Laboratoire PRISME

Titre : Non-astymptotic pseudo-state estimation for a class of fractional order linear systems.

Résumé: This paper aims at designing a non-asymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's observable canonical form of pseudo-state space representation with unknown initial conditions. Firstly, this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output, based on which the modulating functions method is applied. Then, the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to non-asymptotically estimate the pseudo-state of the system in noisy environment. Secondly, the pseudo-state estimator is studied in discrete noisy case, which contains the numerical error due to a used numerical integration method, and the noise error contribution due to a class of stochastic processes. Then, the noise error contribution is analyzed, where an error bound useful for the selection of design parameter is provided. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator, where some comparisons with the fractional order Luenberger-like observer and a new fractional order H_infty-like observer are given.

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10h05-10h50: Daniele Astolfi

University of Bologna, Italy

Titre:  Low-power high-gain observers

Résumé: High-gain observers have been extensively used in nonlinear control since the end of the 80’s for their tunability property, namely the fact that the rate of convergence of the observer can be tuned by acting with one single high-gain parameter. This important feature is motivated by the use of observers in output feedback control and it has been proved that this tunability property plays a key role in establishing a nonlinear separation principle. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks. Mainly: numerical issues due to the fact that we need to implement coefficients which increases polynomially with the system dimension; the well-known peaking phenomenon; high sensitivity to measurement noise. Motivated by these considerations, we propose a new class of nonlinear high-gain observers, denoted as “low-power high-gain observers”, that preserves the same high-gain features but which substantially overtakes (or improves) the aforementioned drawbacks. The low-power high-gain observers are characterized by having coefficients which does not grow with the system dimension, by avoiding the peaking phenomenon and by improving the sensitivity to high-frequency measurement noise. The proposed observers can be used without loss of generality with respect to standard high-gain observers in frameworks of observations, output feedback or output regulation.

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10h55-11h40:   Lucien Etienne, Laurent Hetel

CRIStal, Lille

Titre : Observer synthesis under time-varying sampling for Lipschitz nonlinear systems

Résumé: The problem of observation of continuous-time nonlinear Lipschitz systems under time-varying discrete measurements are studied.
This class of systems naturally occurs when continuous processes are observed through digital sensors and information is sent via a network to a computer for state estimation.
Since network introduces uncertainties in the sampling time, the observer must be designed so to take these uncertainties into account.
Here impulsive observers, which make instantaneous correction when information is received, are investigated.
Since both continuous-time and discrete-time dynamics are involved, the hybrid systems formalism is used to state the problem and establish the convergence of the proposed observer. First, generic conditions are provided using a hybrid Lyapunov function. Then a restriction of the generic Lyapunov function is used to establish tractable conditions that allows the synthesis of an impulsive gain.