<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Publié en ligne: 11 janv. 2019

Pages: 649 - 659

Reçu: 05 mars 2018

Accepté: 14 juil. 2018

DOI: https://doi.org/10.2478/amcs-2018-0050

Mots clés
noninteger-order systems, heat transfer equation, infinite dimensional systems, continuous fraction expansion, stability

© 2019 Krzysztof Oprzędkiewicz, Wojciech Mitkowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Publié en ligne: 11 janv. 2019

Pages: 649 - 659

Reçu: 05 mars 2018

Accepté: 14 juil. 2018

DOI: https://doi.org/10.2478/amcs-2018-0050

Mots clésnoninteger-order systems, heat transfer equation, infinite dimensional systems, continuous fraction expansion, stability

© 2019 Krzysztof Oprzędkiewicz, Wojciech Mitkowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
noninteger-order systems, heat transfer equation, infinite dimensional systems, continuous fraction expansion, stability