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Admissible Solution

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Augusto Ferrante – One of the best experts on this subject based on the ideXlab platform.

  • Minimal resources identifiability and estimation of quantum channels
    Quantum Information Processing, 2014
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We characterize and discuss the identifiability condition for quantum process tomography, as well as the minimal experimental resources that ensure a unique Solution in the estimation of quantum channels, with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulation is provided to support the results and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • CDC – Estimation of quantum channels: Identifiability and ML methods
    2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • On Quantum Channel Estimation with Minimal Resources
    arXiv: Quantum Physics, 2011
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

Mattia Zorzi – One of the best experts on this subject based on the ideXlab platform.

  • Minimal resources identifiability and estimation of quantum channels
    Quantum Information Processing, 2014
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We characterize and discuss the identifiability condition for quantum process tomography, as well as the minimal experimental resources that ensure a unique Solution in the estimation of quantum channels, with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulation is provided to support the results and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • CDC – Estimation of quantum channels: Identifiability and ML methods
    2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • On Quantum Channel Estimation with Minimal Resources
    arXiv: Quantum Physics, 2011
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

Francesco Ticozzi – One of the best experts on this subject based on the ideXlab platform.

  • Minimal resources identifiability and estimation of quantum channels
    Quantum Information Processing, 2014
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We characterize and discuss the identifiability condition for quantum process tomography, as well as the minimal experimental resources that ensure a unique Solution in the estimation of quantum channels, with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulation is provided to support the results and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • CDC – Estimation of quantum channels: Identifiability and ML methods
    2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

  • On Quantum Channel Estimation with Minimal Resources
    arXiv: Quantum Physics, 2011
    Co-Authors: Mattia Zorzi, Francesco Ticozzi, Augusto Ferrante
    Abstract:

    We determine the minimal experimental resources that ensure a unique Solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically Admissible Solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

Philippe Weber – One of the best experts on this subject based on the ideXlab platform.

  • Reconfigurability analysis for reliable fault-tolerant control design
    International Journal of Applied Mathematics and Computer Science, 2011
    Co-Authors: Ahmed Khelassi, Didier Theilliol, Philippe Weber
    Abstract:

    In this paper the integration of reliability evaluation in reconfigurability analysis of a fault-tolerant control system is considered. The aim of this work is to contribute to reliable fault-tolerant control design. The admissibility of control reconfigurability is analyzed with respect to reliability requirements. This analysis shows the relationship between reliability and control reconfigurability defined generally through Gramian controllability. An Admissible Solution for reconfigurability is proposed according to reliability evaluation based on energy consumption under degraded functional conditions. The proposed study is illustrated with a flight control application.

  • Reconfigurability analysis for reliable fault-tolerant control design
    , 2009
    Co-Authors: Ahmed Khelassi, Didier Theilliol, Philippe Weber
    Abstract:

    This paper interests to the reconfigurability of fault-tolerant control system based on the reliability analysis of components. The aim of this work is to present the need of reliability analysis in fault-tolerant control design. The admissibility of system reconfigurability with respect to the reliability constraints is considered in this research. This analysis proves that the control reconfigurability is a system property that not only related to the Gramian controllability but also to the overall system reliability. An Admissible Solution for reconfigurability indicator generation is proposed according to the reliability evaluation in degraded mode. A linearized aircraft model is considered as an example to illustrate this approach.

Ludovic Chamoin – One of the best experts on this subject based on the ideXlab platform.

  • An a posteriori verification procedure for PGD reduced models
    , 2015
    Co-Authors: Pierre-eric Allier, Ludovic Chamoin, Pierre Ladevèze
    Abstract:

    Despite the important progress in computer sciences, the cost associated with the reSolution of multi-parametric problems can be extremely prohibitive. This is especially important when dealing with problems depending on numerous parameters, as encountered in optimization studies which are becoming more and more mandatory for the design of new products. Reduced Order Modelling (ROM) are a good answer to circumvent this issue, usually called curse of dimensionality. However, the main drawback of ROM is the lack of a robust error estimator to measure the quality of the approximated Solution, even if several a priori and a posteriori error estimators for them have already been proposed. This paper defines an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques, a particularly promising technique which is currently the subject of many research activities. Because of the absence of PGD’s error estimator in the literatures, such procedure is a first one. Using the concept of constitutive relation error, we show that we can get guaranteed global/goal-oriented error estimator taking both discretization and PGD truncation error into accounts. By splitting the errors sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximation. The key point of that method is the construction of an Admissible Solution by only post-processing the PGD one, allowing the reuse of classical constitutive relation error technique initially developed for the finite element methods. The focus of the talk is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds; (ii) error splitting and adaptive process when performing PGD-based model reduction.

  • A New PGD Approximation: Computation and Verification
    , 2014
    Co-Authors: Pierre-eric Allier, Ludovic Chamoin, Pierre Ladevèze
    Abstract:

    In this paper, a proper generalized decomposition (PGD) model reduction strategy is defined which is controlled and driven by means of the constitutive relation error (CRE). Because the main drawback of the PGD technique is the absence of a robust a posteriori error estimator to measure the quality of the approximate Solution, such a strategy allows to use the power of the CRE to take into account all sources of error such as the discretization and modal truncation ones. The key point of that method is the construction of an Admissible Solution by post-processing the PGD one. To reuse the classical CRE technique, a first step consists of establishing a Solution that respects the finite element equilibration. The main and only difficulty with the PGDapproximations is that they do not satisfy the finite element equilibrium. Then, to overcome this difficulty, a rather simple technique, is proposed, which associates the PGD-approximation and the data to a new approximation able to enter in the CREmachinery. Then the specific error indicators can be used in an adaptive strategy to construct a guaranteed Solution up to a specific precision, and therefore to provide for reliable virtual charts for engineering design purposes.

  • Robust control of PGD-based reduced models
    , 2012
    Co-Authors: Ludovic Chamoin, Pierre Ladevèze, Florent Pled
    Abstract:

    Nowadays, numerical simulation constitutes a common tool in science and engineering activities; it is especially used for prediction, decision making, or simply for a better understanding of physical phenomena. However, in order to give an accurate representation of the real world, a large set of parameters may need to be introduced in the mathematical models involved in the simulation, which leads to a huge number of degrees of freedom (due to the so-called curse of dimensionality) if classical brute force methods are employed. In this context, model reduction methods are necessary in order to avoid important (and often overwhelming) computational efforts. During the last few years, appealing model reduction techniques, based on separation of variables within a spectral reSolution approach (such as the POD), have received a growing interest. In particular, a technique called Proper Generalized Decomposition (PGD) has been very recently introduced as a POD extension. Contrary to the POD, the PGD approximation does not require any knowledge on the Solution (it is thus referred as a priori ); it operates in an iterative strategy in which a set of simple problems, that can be seen as pseudo eigenvalue problems, need to be solved. However, even though the PGD is usually very effective, a major drawback is that it does not include, until now, any robust error estimate that could give an idea of the quality of the approximate Solution. In the present work, we introduce a consistent error estimator for numerical simulations performed by means of the Proper Generalized Decomposition (PGD) approximation. This estimator, which is based on the constitutive relation error, enables to capture all error sources (i.e. those coming from space and time numerical discretizations, from the truncation of the PGD decomposition, etc. . . ) and leads to guaranteed bounds on the exact error. The specificity of the associated method is a double approach, i.e. a kinematic approach and a unusual static approach, for solving the parameterized problem by means of PGD. This last approach makes straightforward the computation of a statically Admissible Solution, which is necessary for robust error estimation. An attractive feature of the error estimator we set up is that it is obtained by means of classical procedures available in finite element codes; it thus represents a practical and relevant tool for driving algorithms carried out in PGD, being possibly used as a stopping criterion or as an adaptation indicator. Numerical experiments on multi-parameter elasticity or transient thermal problems illustrate the performances of the proposed method for global and goal-oriented error estimation.