Observability

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Christian Commault - One of the best experts on this subject based on the ideXlab platform.

  • Observability in Connected Strongly Regular Graphs and Distance Regular Graphs
    IEEE Transactions on Control of Network Systems, 2014
    Co-Authors: Alain Y. Kibangou, Christian Commault
    Abstract:

    This paper concerns the study of Observability in consensus networks modeled with strongly regular graphs or distance regular graphs. We first give a Kalman-like simple algebraic criterion for Observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we define some bipartite graphs that capture the Observability properties of the graph to be studied. In particular, we show that necessary and sufficient Observability conditions are given by the nullity of the so-called local bipartite Observability graph (resp. local unfolded bipartite Observability graph) for strongly regular graphs (resp. distance regular graphs). When the nullity cannot be derived directly from the structure of these bipartite graphs, the rank of the associated bi-adjacency matrix allows evaluating Observability. Eventually, as a by-product of the main results we show that non-Observability can be stated just by comparing the valency of the graph to be studied with a bound computed from the number of vertices of the graph and its diameter. Similarly nonObservability can also be stated by evaluating the size of the maximum matching in the above mentioned bipartite graphs.

  • Observability in Connected Strongly Regular Graphs and Distance Regular Graphs
    IEEE Transactions on Control of Network Systems, 2014
    Co-Authors: Alain Y. Kibangou, Christian Commault
    Abstract:

    This paper concerns the study of Observability in consensus networks modeled with strongly regular graphs or distance regular graphs. We first give a Kalman-like simple algebraic criterion for Observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we define some bipartite graphs that capture the Observability properties of the graph to be studied. In particular, we show that necessary and sufficient Observability conditions are given by the nullity of the so-called local bipartite Observability graph (respectively, the local unfolded bipartite Observability graph) for strongly regular graphs (respectively, the distance regular graphs). When the nullity cannot be derived directly from the structure of these bipartite graphs, the rank of the associated bi-adjacency matrix enables evaluating Observability. Eventually, as a byproduct of the main results, we show that nonObservability can be stated just by comparing the valency of the graph to be studied with a bound computed from the number of vertices of the graph and its diameter. Similarly, nonObservability can also be stated by evaluating the size of the maximum matching in the aforementioned bipartite graphs.

  • Sensor classification for Observability preservation under sensor failure
    IFAC Proceedings Volumes (IFAC-PapersOnline), 2009
    Co-Authors: Christian Commault, Trong Hieu Do, Jean-michel Dion, Do-hieu Trinh
    Abstract:

    This paper is concerned with the classification of sensors with respect to their importance for Observability preservation under sensor failure. We consider linear observable systems and we wonder if a given system remains observable in case of sensor failure. In a previous work, the critical sensors, called essential, which failure leads to Observability loss have been defined, as well as the useless ones, which may fail without impacting system Observability. The main contribution of this paper is to provide with a refined classification of sensors for Observability. For this purpose we define for each sensor a criticity degree related with its importance for Observability preservation in case of sensor failure. The larger the criticity degree is, the worst for Observability preservation in case of failure of this sensor. We use a network which represents all the possible situations in case of sensor failure, and we will exhibit a reduced network which captures all the relevant information. On this reduced network, we will easily associate with each sensor a quantitative measure of the seriousness of its possible failure. © 2009 IFAC.

  • Observability preservation under sensor failure
    2006
    Co-Authors: Christian Commault, Jean-michel Dion, Do-hieu Trinh
    Abstract:

    This paper is concerned with the study of Observability in a structured framework. It turns out that the system is structurally observable if and only if the system is output connected and contains no contraction. We focus our attention on the Observability preservation under sensor failure. We consider linear observable systems and we wonder if a given system remains observable in case of sensor failure. More precisely we will characterize among the sensors those which are critical \emph{i.e.} which failure leads to Observability loss, those which are useless for Observability purpose and the set of those which are useful without being critical. Using a graph approach we classify the sensors with respect to their importance for output connection preservation, contraction avoidance and then Observability preservation under sensor failure.

Jean-pierre Barbot - One of the best experts on this subject based on the ideXlab platform.

  • Influence of the singular manifold of non observable states in reconstructing chaotic attractors
    Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2012
    Co-Authors: Madalin Frunzete, Jean-pierre Barbot, Christophe Letellier
    Abstract:

    It is known that the reconstructed phase portrait of a given system strongly depends on the choice of the observable. In particular, the ability to obtain a global model from a time series strongly depends on the Observability provided by the measured variable. Such a dependency results from i) the existence of a singular Observability manifold for which the coordinate transformation ii) how often the trajectory visits the neighborhood of the Observability singularity manifold (OSM). In order to clarify how these aspects contribute to the Observability coefficients, we introduce the probability of visits of OSM and the relative time spent in OSM to construct a new coefficient. Combined with the symbolic Observability coefficients previously introduced by one of the authors.

  • ZTN Observability FOR PARALLEL MULTI-CELL CHOPPER
    2011
    Co-Authors: Bilal Amghar, Moumen Darcherif, Jean-pierre Barbot
    Abstract:

    In most industrial processes that use electrical energy as a source of tension or current, requiring a power circuit to control of these physical states.This paper deals with Observability problems of the parallel multi-cell chopper. This type of choppers is a new DC/DC static power converter. After modeling of the power converter, its hybrid dynamical behavior and properties are highlighted. The Observability properties of the state vector is studied from the new Observability concept ( The Z(TN)- Observability ). Following this Observability analysis an adequate sensor placement is proposed after an Observability analysis and a super-twisting observer has been proposed, that ensures finite-time convergence and robustness under bounded perturbations. That is why, its estimation by means of an observer becomes an attractive and economical solution. The suitability of the proposed strategy is proved by extensive computer aided simulations employing a comprehensive model of the system considering noisy measurements and load variations.

  • Observability analysis for parallel multi-cell chopper
    2011
    Co-Authors: Bilal Amghar, Moumen Darcherif, Jean-pierre Barbot
    Abstract:

    This paper deals with Observability problems of the parallel multi-cell chopper. This type of choppers is a new DC/DC static power converter which has an output current equals to n times the source current where n is the number of cells. After recalling the dynamical equations of the converter, its hybrid dynamical behavior and properties are highlighted. This particular hybrid system induces new and difficult Observability problems, such problem can be tackled by a new Observability concept (The Z(TN)-Observability). Following this Observability analysis an adequate sensor placement is proposed after an Observability analysis and high order sliding mode observer designs are proposed. It is important to note that the use of physical extra sensors in order to measure the current in each phases increases the cost and the complexity of the system. That is why, its estimation by means of an observer becomes an attractive and economical solution. Our approaches are attested by several numerical simulations considering noisy measurements and load variations.

  • Synchronous Motor Observability Study and an Improved Zero-speed Position Estimation Design
    2010
    Co-Authors: Dalila Zaltni, Malek Ghanes, Jean-pierre Barbot, Abdelkrim Naceur
    Abstract:

    This paper deals with the Permanent Magnet Synchronous Motor (PMSM) Observability analysis for sensorless control design. The problem of loss of Observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical Observability analyses for the PMSM. In the literature, only the sufficient Observability condition has been presented. Therefore, the current work is aimed especially to the necessary Observability condition analysis. Furthermore, an Estimator/Observer Swapping system is designed here for the surface Permanent Magnet SynchronousMotor (PMSM) to overcome position Observability problems at zero speed which is an unobservable state point.

  • On the Observability of Nonlinear and Switched Systems
    Emergent Problems in Nonlinear Systems and Control, 2009
    Co-Authors: Wei Kang, Jean-pierre Barbot
    Abstract:

    In this paper, new concept of Observability are introduced for both nonlinear systems and switched systems. The new definitions are applicable to a much broader family of problems of estimation including unmeasured state variables, unknown input, and unknown parameters in control systems. It is also taken into account the notion of partial Observability which is useful for complex or networked systems. For switched systems, the relationship between the Observability and hybrid time trajectories is analyzed. It is proved that a switched system might be observable even when individual subsystems are not. Another topic addressed in this paper is the measure of Observability, which is able to quantitatively define the robustness and the precision of Observability. It is shown that a system can be perfectly observable in the traditional sense, but in the case of high dimensions, it is practically unobservable (or extremely weekly observable). Moreover, computational algorithm for nonlinear systems is developed to compute the Observability with precision. Several examples are given to illustrate the fundamentals and the usefulness of the results.

Christophe Letellier - One of the best experts on this subject based on the ideXlab platform.

  • assessing Observability of chaotic systems using delay differential analysis
    arXiv: Adaptation and Self-Organizing Systems, 2020
    Co-Authors: Christopher E Gonzalez, Claudia Lainscsek, Terrence J Sejnowski, Christophe Letellier
    Abstract:

    Observability can determine which recorded variables of a given system are optimal for discriminating its different states. Quantifying Observability requires knowledge of the equations governing the dynamics. These equations are often unknown when experimental data are considered. Consequently, we propose an approach for numerically assessing Observability using Delay Differential Analysis (DDA). Given a time series, DDA uses a delay differential equation for approximating the measured data. The lower the least squares error between the predicted and recorded data, the higher the Observability. We thus rank the variables of several chaotic systems according to their corresponding least square error to assess Observability. The performance of our approach is evaluated by comparison with the ranking provided by the symbolic Observability coefficients as well as with two other data-based approaches using reservoir computing and singular value decomposition of the reconstructed space. We investigate the robustness of our approach against noise contamination.

  • Structural, dynamical and symbolic Observability: From dynamical systems to networks
    PLoS ONE, 2018
    Co-Authors: Luis A. Aguirre, Leonardo Portes, Christophe Letellier
    Abstract:

    Classical definitions of Observability classify a system as either being observable or not. Observability has been recognized as an important feature to study complex networks, and as for dynamical systems the focus has been on determining conditions for a network to be observable. About twenty years ago continuous measures of Observability for nonlinear dynamical systems started to be used. In this paper various aspects of Observability that are established for dynamical systems will be investigated in the context of networks. In particular it will be discussed in which ways simple networks can be ranked in terms of Observability using continuous measures of such a property. Also it is pointed out that the analysis of the network topology is typically not sufficient for Observability purposes, since both the dynamics and the coupling of such nodes play a vital role. Some of the main ideas are illustrated by means of numerical simulations.

  • Observability and synchronization of neuron models
    Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017
    Co-Authors: Luis Aguirre, Leonardo L. Portes, Christophe Letellier
    Abstract:

    Observability is the property that enables recovering the state of a dynamical system from a reduced number of measured variables. In high-dimensional systems, it is therefore important to make sure that the variable recorded to perform the analysis conveys good Observability of the system dynamics. The Observability of a network of neuron models depends nontrivially on the Observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, to perform a study of Observability using four well-known neuron models by computing three different Observability coefficients. This not only clarifies Observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, to study the emergence of phase synchronization in networks composed of neuron models. This is done performing multivariate singular spectrum analysis which, to the best of the authors' knowledge, has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization: (i) without having to measure all the state variables, but only one (that provides greatest Observability) from each node and (ii) without having to estimate the phase. Published by AIP Publishing. https://doi.

  • Symbolic computations of nonlinear Observability
    Physical Review E, 2015
    Co-Authors: Ezequiel Bianco-martinez, Murilo S. Baptista, Christophe Letellier
    Abstract:

    Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of Observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome this difficulty, we introduce here a symbolic Observability coefficient based on a symbolic computation of the determinant of the Observability matrix. The computation of such coefficients is straightforward and can be easily analytically carried out, as demonstrated in this paper for a five-dimensional rational system.

  • Influence of the singular manifold of non observable states in reconstructing chaotic attractors
    Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2012
    Co-Authors: Madalin Frunzete, Jean-pierre Barbot, Christophe Letellier
    Abstract:

    It is known that the reconstructed phase portrait of a given system strongly depends on the choice of the observable. In particular, the ability to obtain a global model from a time series strongly depends on the Observability provided by the measured variable. Such a dependency results from i) the existence of a singular Observability manifold for which the coordinate transformation ii) how often the trajectory visits the neighborhood of the Observability singularity manifold (OSM). In order to clarify how these aspects contribute to the Observability coefficients, we introduce the probability of visits of OSM and the relative time spent in OSM to construct a new coefficient. Combined with the symbolic Observability coefficients previously introduced by one of the authors.

Alain Y. Kibangou - One of the best experts on this subject based on the ideXlab platform.

  • Observability in Connected Strongly Regular Graphs and Distance Regular Graphs
    IEEE Transactions on Control of Network Systems, 2014
    Co-Authors: Alain Y. Kibangou, Christian Commault
    Abstract:

    This paper concerns the study of Observability in consensus networks modeled with strongly regular graphs or distance regular graphs. We first give a Kalman-like simple algebraic criterion for Observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we define some bipartite graphs that capture the Observability properties of the graph to be studied. In particular, we show that necessary and sufficient Observability conditions are given by the nullity of the so-called local bipartite Observability graph (resp. local unfolded bipartite Observability graph) for strongly regular graphs (resp. distance regular graphs). When the nullity cannot be derived directly from the structure of these bipartite graphs, the rank of the associated bi-adjacency matrix allows evaluating Observability. Eventually, as a by-product of the main results we show that non-Observability can be stated just by comparing the valency of the graph to be studied with a bound computed from the number of vertices of the graph and its diameter. Similarly nonObservability can also be stated by evaluating the size of the maximum matching in the above mentioned bipartite graphs.

  • Observability in Connected Strongly Regular Graphs and Distance Regular Graphs
    IEEE Transactions on Control of Network Systems, 2014
    Co-Authors: Alain Y. Kibangou, Christian Commault
    Abstract:

    This paper concerns the study of Observability in consensus networks modeled with strongly regular graphs or distance regular graphs. We first give a Kalman-like simple algebraic criterion for Observability in distance regular graphs. This criterion consists in evaluating the rank of a matrix built with the components of the Bose-Mesner algebra associated with the considered graph. Then, we define some bipartite graphs that capture the Observability properties of the graph to be studied. In particular, we show that necessary and sufficient Observability conditions are given by the nullity of the so-called local bipartite Observability graph (respectively, the local unfolded bipartite Observability graph) for strongly regular graphs (respectively, the distance regular graphs). When the nullity cannot be derived directly from the structure of these bipartite graphs, the rank of the associated bi-adjacency matrix enables evaluating Observability. Eventually, as a byproduct of the main results, we show that nonObservability can be stated just by comparing the valency of the graph to be studied with a bound computed from the number of vertices of the graph and its diameter. Similarly, nonObservability can also be stated by evaluating the size of the maximum matching in the aforementioned bipartite graphs.

W M Wonham - One of the best experts on this subject based on the ideXlab platform.

  • relative Observability of discrete event systems and its supremal sublanguages
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Renyuan Zhang, W M Wonham
    Abstract:

    We identify a new Observability concept, called relative Observability, in supervisory control of discrete-event systems under partial observation. A fixed, ambient language is given, relative to which Observability is tested. Relative Observability is stronger than Observability, but enjoys the important property that it is preserved under set union; hence there exists the supremal relatively observable sublanguage of a given language. Relative Observability is weaker than normality, and thus yields, when combined with controllability, a generally larger controlled behavior; in particular, no constraint is imposed that only observable controllable events may be disabled. We design new algorithms which compute the supremal relatively observable (and controllable) sublanguage of a given language, which is generally larger than the normal counterpart. We demonstrate the new Observability concept and algorithms with a Guideway and an AGV example.

  • Supervisory control of timed discrete-event systems under partial observation
    IEEE Transactions on Automatic Control, 1995
    Co-Authors: Feng Lin, W M Wonham
    Abstract:

    This paper extends the authors' previous work on Observability of discrete-event systems by taking time into consideration. In a timed discrete-event system, events must occur within their respective lower and upper time bounds. A supervisor can disable, enable, or force some events to achieve a given control objective. The authors assume that the supervisor does not observe all events, which is often the case in practice. The authors generalize the concept of Observability to timed discrete-event systems and show that it characterizes the existence condition for a supervisor. The authors also generalize normality, a stronger version of Observability, to timed discrete-event systems, which has nice properties that are absent in Observability. The authors then derive conditions under which Observability and normality are equivalent. The authors propose two methods to synthesize a supervisor, a direct approach and an indirect approach. An example is given to illustrate the results. >