Reconstruction Error

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Jamal Daafouz - One of the best experts on this subject based on the ideXlab platform.

  • Bounded State Reconstruction Error for LPV Systems With Estimated Parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    The note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IFAC Proceedings Volumes, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    Abstract This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available, the special situation when the parameters are estimated with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of Input-to-State Stability. An illustrative example borrowed from the chaos synchronization problem is given.

Gilles Millerioux - One of the best experts on this subject based on the ideXlab platform.

  • Bounded State Reconstruction Error for LPV Systems With Estimated Parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    The note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IFAC Proceedings Volumes, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    Abstract This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available, the special situation when the parameters are estimated with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of Input-to-State Stability. An illustrative example borrowed from the chaos synchronization problem is given.

Matthias Hein - One of the best experts on this subject based on the ideXlab platform.

  • Robust PCA: Optimization of the Robust Reconstruction Error over the Stiefel Manifold
    arXiv: Machine Learning, 2015
    Co-Authors: Anastasia Podosinnikova, Simon Setzer, Matthias Hein
    Abstract:

    It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed Reconstruction Error. By directly minimizing over the Stiefel manifold, we avoid deflation as often used by projection pursuit methods. In distinction to other methods for robust PCA, our method has no free parameter and is computationally very efficient. We illustrate the performance on various datasets including an application to background modeling and subtraction. Our method performs better or similar to current state-of-the-art methods while being faster.

  • GCPR - Robust PCA: Optimization of the Robust Reconstruction Error Over the Stiefel Manifold
    Lecture Notes in Computer Science, 2014
    Co-Authors: Anastasia Podosinnikova, Simon Setzer, Matthias Hein
    Abstract:

    It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed Reconstruction Error. By directly minimizing over the Stiefel manifold, we avoid deflation as often used by projection pursuit methods. In distinction to other methods for robust PCA, our method has no free parameter and is computationally very efficient. We illustrate the performance on various datasets including an application to background modeling and subtraction. Our method performs better or similar to current state-of-the-art methods while being faster.

Gérard Bloch - One of the best experts on this subject based on the ideXlab platform.

  • Bounded State Reconstruction Error for LPV Systems With Estimated Parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    The note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IFAC Proceedings Volumes, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    Abstract This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available, the special situation when the parameters are estimated with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of Input-to-State Stability. An illustrative example borrowed from the chaos synchronization problem is given.

Lionel Rosier - One of the best experts on this subject based on the ideXlab platform.

  • Bounded State Reconstruction Error for LPV Systems With Estimated Parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IEEE Transactions on Automatic Control, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    The note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.

  • Bounded state Reconstruction Error for LPV systems with estimated parameters
    IFAC Proceedings Volumes, 2004
    Co-Authors: Gilles Millerioux, Lionel Rosier, Gérard Bloch, Jamal Daafouz
    Abstract:

    Abstract This note deals with the state Reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available, the special situation when the parameters are estimated with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state Reconstruction Error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of Input-to-State Stability. An illustrative example borrowed from the chaos synchronization problem is given.