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Karny M.,Czech Institute of Information Theory And Automation
Information Sciences | Year: 2016

A high-order Markov chain is a universal model of stochastic relations between discrete-valued variables. The exact estimation of its transition probabilities suffers from the curse of dimensionality. It requires an excessive amount of informative observations as well as an extreme memory for storing the corresponding sufficient statistic. The paper bypasses this problem by considering a rich subset of Markov-chain models, namely, mixtures of low dimensional Markov chains, possibly with external variables. It uses Bayesian approximate estimation suitable for a subsequent decision making under uncertainty. The proposed recursive (sequential, one-pass) estimator updates a product of Dirichlet probability densities (pds) used as an approximate posterior pd, projects the result back to this class of pds and applies an improved data-dependent stabilised forgetting, which counteracts the dangerous accumulation of approximation errors. © 2015 Elsevier Inc. All rights reserved.

Bakule L.,Czech Institute of Information Theory And Automation
Annual Reviews in Control | Year: 2014

This paper reviews state of the art in the area of decentralized networked control systems with an emphasis on event-triggered approach. The models or agents with the dynamics of linear continuous-time time-invariant state-space systems are considered. They serve for the framework for network phenomena within two basic structures. The I/O-oriented systems as well as the interaction-oriented systems with disjoint subsystems are distinguished. The focus is laid on the presentation of recent decentralized control design and co-design methods which offer effective tools to overcome specific difficulties caused mainly by network imperfections. Such side-effects include communication constraints, variable sampling, time-varying transmission delays, packet dropouts, and quantizations. Decentralized time-triggered methods are briefly discussed. The review is deals mainly with decentralized event-triggered methods. Particularly, the stabilizing controller-observer event-based controller design as well as the decentralized state controller co-design are presented within the I/O-oriented structures of large scale complex systems. The sampling instants depend in this case only on a local information offered by the local feedback loops. Minimum sampling time conditions are discussed. Special attention is focused on interaction-oriented system architecture. Model-based approach combined with event-based state feedback controller design is presented, where the event thresholds are fully decentralized. Finally, several selected open decentralized control problems are briefly offered as recent research challenges. © 2014 Elsevier Ltd. All rights reserved.

Kroupa T.,Czech Institute of Information Theory And Automation
International Journal of Approximate Reasoning | Year: 2012

It will be shown that probabilities of infinite-valued events represented by formulas in Łukasiewicz propositional logic are in one-to-one correspondence with tight probability measures over rational polyhedra in the unit hypercube. This result generalizes a recent work on rational measures of polyhedra and provides an elementary geometric approach to reasoning under uncertainty with states in Łukasiewicz logic. © 2011 Elsevier Inc. All rights reserved.

Karny M.,Czech Institute of Information Theory And Automation
Information Sciences | Year: 2014

Bayesian learning provides a firm theoretical basis of the design and exploitation of algorithms in data-streams processing (preprocessing, change detection, hypothesis testing, clustering, etc.). Primarily, it relies on a recursive parameter estimation of a firmly bounded complexity. As a rule, it has to approximate the exact posterior probability density (pd), which comprises unreduced information about the estimated parameter. In the recursive treatment of the data stream, the latest approximate pd is usually updated using the treated parametric model and the newest data and then approximated. The fact that approximation errors may accumulate over time course is mostly neglected in the estimator design and, at most, checked ex post. The paper inspects the estimator design with respect to the error accumulation and concludes that a sort of forgetting (pd flattening) is an indispensable part of a reliable approximate recursive estimation. The conclusion results from a Bayesian problem formulation complemented by the minimum Kullback-Leibler divergence principle. Claims of the paper are supported by a straightforward analysis, by elaboration of the proposed estimator to widely applicable parametric models and illustrated numerically. © 2014 Elsevier Inc. All rights reserved.

Kroupa T.,Czech Institute of Information Theory And Automation
Soft Computing | Year: 2012

We generalise belief functions to many-valued events which are represented by elements of Lindenbaum algebra of infinite-valued Łukasiewicz propositional logic. Our approach is based on mass assignments used in the Dempster-Shafer theory of evidence. A generalised belief function is totally monotone and it has Choquet integral representation with respect to a unique belief measure on Boolean events. © 2012 Springer-Verlag.

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