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Exponential H ∞ filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays

Li Ma, Meimei Xu, Ruting Jia, Hui Ye (2014)

Kybernetika

This paper is concerned with the exponential H ∞ filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and H ∞ control problem. Then, a mean-square...

H ∞ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities

Lingchun Li, Guangming Zhang, Meiying Ou, Yujie Wang (2019)

Kybernetika

This paper is devoted to design H ∞ sliding mode controller for continuous-time Markov jump systems with interval time-varying delays and general transition probabilities. An integral sliding surface is constructed and its reachability is guaranteed via a sliding mode control law. Meanwhile, a linearisation strategy is applied to treat the nonlinearity induced by general transition probabilities. Using a separation method based on Finsler lemma to eliminate the coupling among Lyapunov variables and...

Improving prediction models applied in systems monitoring natural hazards and machinery

Marek Sikora, Beata Sikora (2012)

International Journal of Applied Mathematics and Computer Science

A method of combining three analytic techniques including regression rule induction, the k-nearest neighbors method and time series forecasting by means of the ARIMA methodology is presented. A decrease in the forecasting error while solving problems that concern natural hazards and machinery monitoring in coal mines was the main objective of the combined application of these techniques. The M5 algorithm was applied as a basic method of developing prediction models. In spite of an intensive development...

Learning extremal regulator implementation by a stochastic automaton and stochastic approximation theory

Ivan Brůha (1980)

Aplikace matematiky

There exist many different approaches to the investigation of the characteristics of learning system. These approaches use different branches of mathematics and, thus, obtain different results, some of them are too complicated and others do not match the results of practical experiments. This paper presents the modelling of learning systems by means of stochastic automate, mainly one particular model of a learning extremal regulator. The proof of convergence is based on Dvoretzky's Theorem on stochastic...

Learning the naive Bayes classifier with optimization models

Sona Taheri, Musa Mammadov (2013)

International Journal of Applied Mathematics and Computer Science

Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization...

Neuro-rough-fuzzy approach for regression modelling from missing data

Krzysztof Simiński (2012)

International Journal of Applied Mathematics and Computer Science

Real life data sets often suffer from missing data. The neuro-rough-fuzzy systems proposed hitherto often cannot handle such situations. The paper presents a neuro-fuzzy system for data sets with missing values. The proposed solution is a complete neuro-fuzzy system. The system creates a rough fuzzy model from presented data (both full and with missing values) and is able to elaborate the answer for full and missing data examples. The paper also describes the dedicated clustering algorithm. The...

Nonlinear state prediction by separation approach for continuous-discrete stochastic systems

Jaroslav Švácha, Miroslav Šimandl (2008)

Kybernetika

The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker–Planck equation (FPE) and by the Bayesian rule. The stress is laid on the computation of the predictive conditional probability density function from the FPE. The solution of the FPE and its integration into the estimation algorithm is the cornerstone for the whole recursive computation. A new usable numerical scheme for the FPE is...

On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak (1999)

Applicationes Mathematicae

We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].

On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan, Jeong-Hoon Kim (2008)

Kybernetika

In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with L 2 ...

On infinite horizon active fault diagnosis for a class of non-linear non-Gaussian systems

Ivo Punčochář, Miroslav Šimandl (2014)

International Journal of Applied Mathematics and Computer Science

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that...

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