A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process

A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process

A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution o...

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Bibliographic Details
Main Authors: Oprzędkiewicz Krzysztof, Mitkowski Wojciech
Format: Article
Language:English
Published: Sciendo 2018-12-01
Series:International Journal of Applied Mathematics and Computer Science
Subjects:
noninteger-order systems
heat transfer equation
infinite dimensional systems
continuous fraction expansion
stability
Online Access:https://doi.org/10.2478/amcs-2018-0050
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spelling doaj-09dd2c1bebd4454f9d9ee2cde88bf8112021-09-06T19:41:09ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922018-12-0128464965910.2478/amcs-2018-0050amcs-2018-0050A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer ProcessOprzędkiewicz Krzysztof0Mitkowski Wojciech1Department of Automatics and Robotics, AGH University of Science and Technology, al. Mickiewicza 30, 30-079Kraków, PolandDepartment of Automatics and Robotics, AGH University of Science and Technology, al. Mickiewicza 30, 30-079Kraków, PolandA new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.https://doi.org/10.2478/amcs-2018-0050noninteger-order systemsheat transfer equationinfinite dimensional systemscontinuous fraction expansionstability
collection DOAJ
language English
format Article
sources DOAJ
author Oprzędkiewicz Krzysztof
Mitkowski Wojciech
spellingShingle Oprzędkiewicz Krzysztof
Mitkowski Wojciech
A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
International Journal of Applied Mathematics and Computer Science
noninteger-order systems
heat transfer equation
infinite dimensional systems
continuous fraction expansion
stability
author_facet Oprzędkiewicz Krzysztof
Mitkowski Wojciech
author_sort Oprzędkiewicz Krzysztof
title A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
title_short A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
title_full A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
title_fullStr A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
title_full_unstemmed A Memory–Efficient Noninteger–Order Discrete–Time State–Space Model of a Heat Transfer Process
title_sort memory–efficient noninteger–order discrete–time state–space model of a heat transfer process
publisher Sciendo
series International Journal of Applied Mathematics and Computer Science
issn 2083-8492
publishDate 2018-12-01
description A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.
topic noninteger-order systems
heat transfer equation
infinite dimensional systems
continuous fraction expansion
stability
url https://doi.org/10.2478/amcs-2018-0050
work_keys_str_mv AT oprzedkiewiczkrzysztof amemoryefficientnonintegerorderdiscretetimestatespacemodelofaheattransferprocess
AT mitkowskiwojciech amemoryefficientnonintegerorderdiscretetimestatespacemodelofaheattransferprocess
AT oprzedkiewiczkrzysztof memoryefficientnonintegerorderdiscretetimestatespacemodelofaheattransferprocess
AT mitkowskiwojciech memoryefficientnonintegerorderdiscretetimestatespacemodelofaheattransferprocess
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