Fault Identification in Non-Stationary Systems Based on Sliding Mode Observers

The paper is devoted to the problem of fault identification in technical systems described by non-stationary nonlinear dynamic equations under unmatched disturbances. To solve the problem, sliding mode observers are used. The suggested ap- proach is based on the model of the original system of minimal dimension having different sensitivity to the faults and distur- bances in contrast to the traditional approaches to sliding observer design which are based on the original system. Additionally it is assumed that matrices describing such a model have the canonical form and are constant. The main purpose of using such a model is possibility to take into account the non-stationary feature of the systems. As a result, the model has stationary dynamic and non-stationary additional term that allows to promote sliding mode design. Besides, the new approach to design sliding mode observers is suggested. The peculiarity of this approach is that it does not require that original systems should be minimum phase and detectable. According to the traditional approaches stability of the observer is provided by minimum phase and detectability properties. In our approach, stability of the observer is achieved due to the canonical form of the matrices describing the model. In addition, the matching condition is not necessary. This allows to extend a class of systems for which sliding mode observers can be designed. Theoretical results are illustrated by practical example of electric servoactuator.

-modules on rigid analytic spaces III: weak holonomicity and operations

We develop a dimension theory for coadmissible $\widehat {\mathcal {D}}$ -modules on rigid analytic spaces and study those which are of minimal dimension, in analogy to the theory of holonomic $\mathcal {D}$ -modules in the algebraic setting. We discuss a number of pathologies contained in this subcategory (modules of infinite length, infinite-dimensional fibres). We prove stability results for closed immersions and the duality functor, and show that all higher direct images of integrable connections restricted to a Zariski open subspace are coadmissible of minimal dimension. It follows that the local cohomology sheaves $\underline {H}^{i}_Z(\mathcal {M})$ with support in a closed analytic subset $Z$ of $X$ are also coadmissible of minimal dimension for any integrable connection $\mathcal {M}$ on $X$ .

Minimal State-Space Representation of Convolutional Product Codes

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

Virtual Sensors in the Fault Diagnosis Problem

The paper is devoted to the problem of fault diagnosis (isolation and identification) in linear dynamic systems under disturbances. The performances of fault diagnosis depend on the sensors which are in the system under diagnosis. To improve the performances, additional sensors can be applied. But sometimes it is impossible to use such sensors; besides they have low reliability. In this paper, we suggest to use so-called virtual sensors instead of additional ones. To obtain such sensors,Luenberger observers can be used. Such an observer is designed in two steps. On the first step, the model of minimal dimension invariant with respect to the disturbances and estimating a predetermined component of the system state vector and some other components of the system state vector is designed. The second components are necessary to provide stability of the observer by means of generating residual and using feedback. Such components are determined during t he process of the problem solution which is based on the canonical form of matrices describing the model. On the second step, the feedback matrix is found based on the required quality of transient. To obtain this matrix, eigenvalues are selected and coefficients of the characteristic equation are calculated. The rule to find the predetermined component of the system state vector to be estimated by vir tual obser ver is suggested. Theoretical results are illustrated by practical example of well known three tank system.

Detection of Representative Variables in Complex Systems with Interpretable Rules Using Core-Clusters

In this paper, we present a new framework dedicated to the robust detection of representative variables in high dimensional spaces with a potentially limited number of observations. Representative variables are selected by using an original regularization strategy: they are the center of specific variable clusters, denoted CORE-clusters, which respect fully interpretable constraints. Each CORE-cluster indeed contains more than a predefined amount of variables and each pair of its variables has a coherent behavior in the observed data. The key advantage of our regularization strategy is therefore that it only requires to tune two intuitive parameters: the minimal dimension of the CORE-clusters and the minimum level of similarity which gathers their variables. Interpreting the role played by a selected representative variable is additionally obvious as it has a similar observed behaviour as a controlled number of other variables. After introducing and justifying this variable selection formalism, we propose two algorithmic strategies to detect the CORE-clusters, one of them scaling particularly well to high-dimensional data. Results obtained on synthetic as well as real data are finally presented.

On minimal faithful representations of a class of nilpotent lie algebras

In this work we consider 2-step nilradicals of parabolic subalgebras of the simple Lie algebra An and describe a new family of faithful nil-representations of the nilradicals na,c, a,c ? N. We obtain a sharp upper bound for the minimal dimension ?(na,c) and for several pairs (a,c) we obtain ?(na,c).

Heavy operators and hydrodynamic tails

The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators – which are generically expected to create thermal states – can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients C_{HH'L}CHH′L, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. We also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems.

The Influence of Covariance Hankel Matrix Dimension on Algorithms for VARMA Models

Some methods for estimating VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. Some authors suggest taking a larger dimension than theoretically necessary for this matrix. If the data sample is populous enough and the Hankel matrix dimension is unnecessarily large, this may result in an unnecessary number of computations, as well as in worse numerical and statistical results. We provide some theoretical results to know which is the Hankel matrix with the lowest dimension that is theoretically necessary and illustrate, with several simulated VARMA models, that using a dimension of the Hankel matrix greater than the theoretical minimal dimension proposed as valid does not necessarily lead to improved estimates. Although we use two algorithms, our main contributions are independent of the estimation method considered. We note that our paper does not include any comparisons between different algorithms for estimating VARMA models, as this is not our aim.