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Random projection RBF nets for multidimensional density estimation

Ewa Skubalska-Rafajłowicz (2008)

International Journal of Applied Mathematics and Computer Science

The dimensionality and the amount of data that need to be processed when intensive data streams are observed grow rapidly together with the development of sensors arrays, CCD and CMOS cameras and other devices. The aim of this paper is to propose an approach to dimensionality reduction as a first stage of training RBF nets. As a vehicle for presenting the ideas, the problem of estimating multivariate probability densities is chosen. The linear projection method is briefly surveyed. Using random...

Random projections and hotelling's T² statistics for change detection in high-dimensional data streams

Ewa Skubalska-Rafajłowicz (2013)

International Journal of Applied Mathematics and Computer Science

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of Rn . We examine the random projection method using artificial noisy image sequences as examples.

Range identification for a perspective dynamic system with a single homogeneous observation

Lili Ma, Yangquan Chen, Kevin Moore (2005)

International Journal of Applied Mathematics and Computer Science

Perspective problems arise in machine vision when using a camera to observe the scene. Essential problems include the identification of unknown states and/or unknown parameters from perspective observations. Range identification is used to estimate the states/positions of a moving object with known motion parameters. Range estimation has been discussed in the literature using nonlinear observers with full homogeneous observations derived from the image plane. In this paper, the same range identification...

Recursive identification algorithm for dynamic systems with output backlash and its convergence

Ruili Dong, Qingyuan Tan, Yonghong Tan (2009)

International Journal of Applied Mathematics and Computer Science

This paper proposes a recursive identification method for systems with output backlash that can be described by a pseudoWiener model. In this method, a novel description of the nonlinear part of the system, i.e., backlash, is developed. In this case, the nonlinear system is decomposed into a piecewise linearized model. Then, a modified recursive general identification algorithm (MRGIA) is employed to estimate the parameters of the proposed model. Furthermore, the convergence of the MRGIA for the...

Recursive identification of Wiener systems

Włodzimierz Greblicki (2001)

International Journal of Applied Mathematics and Computer Science

A Wiener system, i.e. a cascade system consisting of a linear dynamic subsystem and a nonlinear memoryless subsystem is identified. The a priori information is nonparametric, i.e. neither the functional form of the nonlinear characteristic nor the order of the dynamic part are known. Both the input signal and the disturbance are Gaussian white random processes. Recursive algorithms to estimate the nonlinear characteristic are proposed and their convergence is shown. Results of numerical simulation...

Recursive self-tuning control of finite Markov chains

Vivek Borkar (1997)

Applicationes Mathematicae

A recursive self-tuning control scheme for finite Markov chains is proposed wherein the unknown parameter is estimated by a stochastic approximation scheme for maximizing the log-likelihood function and the control is obtained via a relative value iteration algorithm. The analysis uses the asymptotic o.d.e.s associated with these.

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau, Dominique Chapelle (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered....

Refracted Lévy processes

A. E. Kyprianou, R. L. Loeffen (2010)

Annales de l'I.H.P. Probabilités et statistiques

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation dUt=−δ1{Ut>b} dt+dXt, where X={Xt : t≥0} is a Lévy...

Rejection of nonharmonic disturbances in nonlinear systems

Shutang Liu, Yuan Jiang, Ping Liu (2010)

Kybernetika

This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm...

Relative cost curves: An alternative to AUC and an extension to 3-class problems

Olga Montvida, Frank Klawonn (2014)

Kybernetika

Performance evaluation of classifiers is a crucial step for selecting the best classifier or the best set of parameters for a classifier. Receiver Operating Characteristic (ROC) curves and Area Under the ROC Curve (AUC) are widely used to analyse performance of a classifier. However, the approach does not take into account that misclassification for different classes might have more or less serious consequences. On the other hand, it is often difficult to specify exactly the consequences or costs...

Relaxed stability conditions for interval type-2 fuzzy-model-based control systems

Tao Zhao, Jian Xiao, Jialin Ding, Xuesong Deng, Song Wang (2014)

Kybernetika

This paper proposes new stability conditions for interval type-2 fuzzy-model-based (FMB) control systems. The type-1 T-S fuzzy model has been widely studied because it can represent a wide class of nonlinear systems. Many favorable results for type-1 T-S fuzzy model have been reported. However, most of conclusions for type-1 T-S fuzzy model can not be applied to nonlinear systems subject to parameter uncertainties. In fact, Most of the practical applications are subject to parameters uncertainties....

Reliability modeling of fault tolerant control systems

Hongbin Li, Qing Zhao, Zhenyu Yang (2007)

International Journal of Applied Mathematics and Computer Science

This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined...

Research problems of Jerzy Zabczyk

Szymon Peszat, Łukasz Stettner (2015)

Banach Center Publications

In the paper we present a selected variety of problems studied by Professor Jerzy Zabczyk. Important part of Prof. Zabczyk's scientific activity was devoted to his PhD students. He has promoted 9 PhD students: Tomasz Bielecki, Jarosław Sobczyk, Łukasz Stettner and Gianmario Tessitore work mostly in control and its applications to mathematical finance, whereas the research of Anna Chojnowska-Michalik, Wojciech Jachimiak, Anna Milian, Szymon Peszat and Anna Rusinek is concentrated mostly on stochastic...

Residual generator fuzzy identification for automotive diesel engine fault diagnosis

Silvio Simani (2013)

International Journal of Applied Mathematics and Computer Science

Safety in dynamic processes is a concern of rising importance, especially if people would be endangered by serious system failure. Moreover, as the control devices which are now exploited to improve the overall performance of processes include both sophisticated control strategies and complex hardware (input-output sensors, actuators, components and processing units), there is an increased probability of faults. As a direct consequence of this, automatic supervision systems should be taken into...

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