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1

Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

Dzieliński A., Czyronis P. M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2013

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Vol. 61, nr 3

681--690

EN

The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.

2

Probabilistic Sequence Mining : Evaluation and Extension of ProMFS Algorithm for Real-Time Problems

Hryniów K., Dzieliński A.

International Journal of Electronics and Telecommunications

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2012

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Vol. 58, No. 4

323-326

EN

Sequential pattern mining is an extensively studied method for data mining. One of new and less documented approaches is estimation of statistical characteristics of sequence for creating model sequences, that can be used to speed up the process of sequence mining. This paper proposes extensive modifications to one of such algorithms, ProMFS (probabilistic algorithm for mining frequent sequences), which notably increases algorithm's processing speed by a significant reduction of its computational complexity. A new version of algorithm is evaluated for real-life and artificial data sets and proven to be useful in real-time applications and problems.

3

Negative feature selection algorithm for anomaly detection in real time

Hryniów K., Dzieliński A.

Studia Informatica : systems and information technology

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2011

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Vol. 1-2(15)

15--23

EN

Anomaly detection methods are of common use in many fields, including databases and large computer systems. This article presents new algorithm based on negative feature selection, which can be used to find anomalies in real time. Proposed algorithm, called Negative Feature Selection algorithm (NegFS) can be also used as first step for preprocessing data analyzed by neural networks, rule-based systems or other anomaly detection tools, to speed up the process for large and very large datasets of different types.

4

Discrete Fractional Order Artificial Neural Network

Sierociuk D., Sarwas G., Dzieliński A.

Acta Mechanica et Automatica

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2011

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Vol. 5, no. 2

128-132

EN

In this paper the discrete time fractional order artificial neural network is presented. This structure is proposed for simulating the dynamics of non-linear fractional order systems. In the second part of this paper several numerical examples are shown. The final part of the paper presents the discussion on the use of fractional or integer discrete time neural network for modelling and simulating fractional order non-linear systems. The simulation results show the advantages of the proposed solution over the classical (integer) neural network approach to modelling of non-linear fractional order systems.

5

Simulation of urban traffic lights control

Amborski K., Dzieliński A., Kowalczuk P.

Logistyka

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2010

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nr 2

EN

Simulation of traffic control is nowadays very important for dealing with increasing urban traffic. It helps to construct the strategy of traffic lights switching and determine alternative path in the case of an accident or traffic jam. In the paper we present the application of simulation tool DYNASIM being prepared by French company DYNALOGIC. It has big number of alternative possibilities in modeling of crossings and conditions. In the paper will be described exemplary simulation of chosen crossings in Warsaw with choice of several different conditions. The simulation package can be free available for universities for educational use.

PL

Symulacja sterowania ruchem drogowym jest obecnie bardzo ważnym elementem w związku z rosnącym ruchem w miastach. Pomaga ona budować strategię działania w ustaleniu przełączeń świateł drogowych i wyznaczaniu alternatywnych dróg transportu w przypadku kolizji lub zatorów. W referacie przedstawiamy zastosowanie narzędzia symulacyjnego DYNASIM przygotowanego przez francuską firmę DYNALOGIC. Oprogramowanie to ma wiele alternatywnych możliwości modelowania skrzyżowań i warunków ruchu. W referacie opisana jest przykładowa symulacja wybranych skrzyżowań w Warszawie z wyborem kilku zestawów warunków. Pakiet symulacyjny może być nieodpłatnie udostępniony uniwersytetom dla celów edukacyjnych.

6

Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation

Sierociuk D., Dzieliński A.

International Journal of Applied Mathematics and Computer Science

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2006

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Vol. 16, no 1

129-140

EN

This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also shows a simple numerical example of linear state estimation. Finally, as an example of nonlinear estimation, the paper discusses the possibility of using these algorithms for parameters and fractional order estimation for fractional order systems. Numerical examples of the use of these algorithms in a general nonlinear case are presented.

7

Stability of a class of adaptive nonlinear systems

Dzieliński A.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

455-462

EN

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.

8

Zastosowanie rekonstrukcji funkcji 2-D do problemu superrozdzielczości

Dzieliński A.

Przegląd Elektrotechniczny

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2002

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R. 78, nr 10

210-213

PL

W artykule przedstawiono rozwiązanie tzw. problemu superrozdzielczości na podstawie wielu ramek obrazu i przy wykorzystaniu algorytmu rekonstrukcji funkcji 2-0. Podano również warunki, które muszą spełniać takie funkcje, aby była możliwa ich rekonstrukcja na podstawie próbek nierównomiernych za pomocą sieci neuropodobnej prostej. Następnie przedyskutowano podejście do rekonstrukcji funkcji wielu zmiennych w oparciu o teorię próbkowania wielowymiarowego. Szczególną uwagę zwrócono na kilka istotnych zagadnień pobocznych, jak np. kwestię rozszerzenia funkcji oraz występujące ograniczenia. W skrócie zaprezentowano metodę rekonstrukcji funkcji na podstawie nierównomiernie rozmieszczonych próbek bazującą na przekształceniu Fouriera. Pokazano, że metoda ta rozwiązuje problem superrozdzielczości.

EN

This paper; is aimed at presenting a solution to the superresolution problem from multiple frames using the 2-0 function reconstruction algorithm. Also, conditions for such functions to be reconstructed from their nonuniform samples by means of feedforward neural networks are given. Further the multidimensional sampling based approach to reconstruction of a multivariable function is discussed. The attention is paid to several important background issues like function extension and restrictions. A Fourier transform based method for function reconstruction out of given nonuniform samples is briefly presented. The method solves the superresolution problem.

9

Modelowanie i sterowanie ukladów nieliniowych metodami neuropodobnymi

Dzieliński A.

Prace Naukowe Politechniki Warszawskiej. Elektryka

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2002

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z. 119

3-184

PL

Rozprawa niniejsza powstała jako wynik prac autora w dziedzinie wykorzystania sieci neuronowych do modelowania i sterowania nieliniowych układów dynamicznych. Celem prac prowadzonych w latach 1992-2001 było zbadanie możliwości wykorzystania sieci neuronowych do modelowania i sterowania adaptacyjnego układami nieliniowymi. Badania były prowadzone w ramach projektów naukowych, realizowanych w Instytucie Sterowania i Elektroniki Przemysłowej Politechniki Warszawskiej oraz w Centre for Systems and Control, University of Glasgow. W pracy przedstawiono gruntowną analizę neuronowego sterowania adaptacyjnego. Podano struktury i algorytmy sieci neuronowych do modelowania, identyfikacji i sterowania nieliniowych układów dynamicznych. Podano również ocenę prezentowanych metod z perspektywy teorii sterowania nieliniowego. Rezultaty prezentowane w pracy mogą służyć za solidną podstawę do opracowania inżynierskiej metodologii projektowania neuronowych układów sterowania adaptacyjnego.

EN

This thesis has emerged as a result of the research, in the area of neural networks application to modelling and control of nonlinear dynamical systems, its author has been involved in. The goal of the research carried on in the years 1992-2001 was to examine the possibilities of applying the neural networks to modelling and adaptive control of nonlinear systems. These were the subjects of several scientific projects successfully completed in the Institute of Control and Industrial Electronics, Warsaw University of Technology and in the Centre for Systems and Control, University of Glasgow. In this book a detailed analysis of neural adaptive systems is presented. Several structures and learning algorithms for modelling, identification and control of nonlinear dynamical systems are given. Also the evaluation of the methods presented is given from the point of view of nonlinear control theory. The results presented in the thesis may serve as a firm foundation for elaboration of an engineering methodology for designing neural, nonlinear, adaptive control systems.

10

Neural Network-Based Narx Models in Non-Linear Adaptive Control

Dzieliński A.

International Journal of Applied Mathematics and Computer Science

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2002

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Vol. 12, no 2

235-240

EN

The applicability of approximate NARX models of non-linear dynamic systems is discussed. The models are obtained by a new version of Fourier analysis-based neural network also described in the paper. This constitutes a reformulation of a known method in a recursive manner, i.e. adapted to account for incoming data on-line. The method allows us to obtain an approximate model of the non-linear system. The estimation of the influence of the modelling error on the discrepancy between the model and real system outputs is given. Possible applications of this approach to the design of BIBO stable closed-loop control are proposed.

11

Difference Inequalities and BIBO Stability of Approximate NARX Models

Dzieliński A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2002

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Vol. 50, Nr 4

295--311

EN

This paper introduces a novel approach to BIBO stability of NARX control systems. The approach is based on difference inequalities and assumes availability of an approximate NARX model and the system order. Sufficient conditions for modelling error are derived ensuring boundedness of the error between model's and plant's outputs for the same inputs. For this class of bounded inputs sufficient conditions for BIBO stability are given and shown practicable. They also allow designing a controller using the model, leading to BIBO stable closed-loop system.