nach oben

Machine Intelligence Research

Erschienen in:

01.06.2015 | Brief Paper

Iterative learning control for discrete parabolic distributed parameter systems

verfasst von: Xi-Sheng Dai, Sen-Ping Tian, Ya-Jun Guo

Erschienen in: Machine Intelligence Research | Ausgabe 3/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, iterative learning control (ILC) technique is applied to a class of discrete parabolic distributed parameter systems described by partial difference equations. A P-type learning control law is established for the system. The ILC of discrete parabolic distributed parameter systems is more complex as 3D dynamics in the time, spatial and iterative domains are involved. To overcome this difficulty, discrete Green formula and analogues discrete Gronwall inequality as well as some other basic analytic techniques are utilized. With rigorous analysis, the proposed intelligent control scheme guarantees the convergence of the tracking error. A numerical example is given to illustrate the effectiveness of the proposed method.

Vorheriger Artikel On the current error based sampled-data iterative learning control with reduced memory capacity

Nächster Artikel Distributed adaptive synchronization of complex dynamical network with unknown time-varying weights

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

[1]

J. Sklansky. Learning systems for automatic control. IEEE Transactions on Automatic Control, vol. 11, no. 1, pp. 6–19, 1966.MathSciNetCrossRef

[2]

K. S. Fun. Learning control systems: Review and outlook. IEEE Transactions on Automatic Control, vol. 15, no. 2, pp. 210–221, 1970.MathSciNetCrossRef

[3]

S. Arimoto, S. Kawamura, F. Miyazaki. Bettering operation of robots by learning. Journal of Robotic Systems, vol.1, no. 2, pp. 123–140, 1984.CrossRef

[4]

S. R. Oh, Z. Bien, I. Suh. An iterative learning control method with application to robot manipulators. IEEE Journal of Robot and Automation, vol. 4, no. 5, pp. 508–514, 1988.CrossRef

[5]

Z. S. Hou, J. X. Xu, H. W. Zhong. Freeway traffic control using iterative learning control based ramp metering and speed signaling. IEEE Transactions on Vehicular Technology, vol. 56, no. 2, pp. 466–477, 2007.CrossRef

[6]

Z. S. Hou, J. X. Xu. Iterative learning control approach for ramp metering. Journal of Control Theory and Applications, vol. 3, no. 1, pp. 27–34, 2005.MathSciNetCrossRef

[7]

Z. S. Hou, S. T. Jin, M. Zhao. Iterative learning identification for the macroscopic traffic. Acta Automatica Sinica, vol. 34, no. 1, pp. 64–71, 2008.MathSciNetCrossRefMATH

[8]

Y. Wang, E. Dassau, F. J. Doyle III. Close-loop control of artificial pancreatic β-cell in type 1 diabetes mellitus using model predictive iterative learning control. IEEE Transactions on Biomedical Engineering, vol. 57, no. 2, pp. 211–219, 2010.CrossRef

[9]

M. X. Sun, B. J. Huang. Iterative Learning Control, Beijing, China: National Defence Industry Press, 1999. (in Chinese)

[10]

S. L. Xie, S. P. Tian, Z. D. Xie. Theory and Application of Iterative Learning Control, Beijing, China: Science Press, pp. 82–102, 2005. (in Chinese)

[11]

H. B. Xu, Z. S. Hou. Stability of iterative learning control with data dropouts via asynchronous dynamical system. International Journal of Automation and Computing, vol.8, no. 1, pp. 29–36, 2011.CrossRef

[12]

D. Li, J. M. Li. Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays and unknown control direction. International Journal of Automation and Computing, vol. 9, no. 6, pp. 578–586, 2012.CrossRef

[13]

Z. Y. Huo, Z. Yang, Y. J. Pang. Set-point-related indirect iterative learning control for multi-input multi-output systems. International Journal of Automation and Computing, vol. 9, no. 3, pp. 266–273, 2012.CrossRef

[14]

R. H. Chi, Z. S. Hou. Dual-stage optimal iterative learning control for nonlinear non-affine discrete-time systems. Acta Automatica Sinica, vol. 32, no. 10, pp. 1061–1065, 2007.MathSciNetCrossRefMATH

[15]

H. F. Chen. Almost sure convergence of iterative learning control for stochastic systems. Science in China (Series F): Information Science, vol. 46, no. 1, pp. 67–70, 2003.MathSciNetCrossRefMATH

[16]

J. H. Choi, B. J. Seo, K. S. Lee. Constrained digital regulation of hyperbolic PDE systems: A learning control approach. Korean Journal of Chemical Engineering, vol. 18, no. 5, pp. 606–611, 2001.CrossRef

[17]

Z. H. Qu. An iterative learning algorithm for boundary control of a stretched moving string. Automatica, vol. 38, no. 5, pp. 821–827, 2002.MathSciNetCrossRefMATH

[18]

C. Xu, A. Reza, S. Eugenio. On iterative learning control of parabolic distributed parameter systems. In Proceedings of the 17th Mediterranean Conference on Control and Automation, IEEE, Thessaloniki, Greece, pp. 510–515, 2009.

[19]

H. Y. Zhao, C. D. Rahn. Iterative learning velocity and tension control for single span axially moving materials. Journal of Dynamic System Measure Control, vol. 130, no. 5, Article number 051003, 2008.

[20]

D. Q. Huang, J. X. Xu. Steady-state iterative learning control for a class of nonlinear PDE processes. Journal of Process Control, vol. 21, no. 8, pp. 1155–1163, 2011.CrossRef

[21]

D. Q. Huang, J. X. Xu, X. F. Li, C. Xu, M. Yu. D-type anticipatory iterative learning control for a class of inhomogeneous heat equations. Automatica, vol. 49, no. 8, pp. 2397–2408, 2013.MathSciNetCrossRef

[22]

B. Cichy, K. Gakowski, E. Rogers. Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization. Multidimensional Systems and Signal Processing, vol. 23, no. 1–2, pp. 185–208, 2012.MathSciNetCrossRefMATH

[23]

B. G. Zhang, Y. Zhou. Qualitative analysis of delay partial difference equations. Contemporary Mathematics and Its Applications, vol. 4, New York, USA: Hindawi Publishing Corporation, 2007.

[24]

S. T. Liu, Y. Q. Liu, F. Q. Deng. Oscillation for nonlinear delay partial difference equations with positive and negative coefficients. Computer and Mathematics with Applications, vol. 43, no. 10–11, pp. 1219–1230, 2002.MathSciNetMATH

[25]

J. Y. W. Patricia, P. A. Ravi. Asymptotic behaviour of solutions of higher order difference and partial difference equations with distributed deviating arguments. Applied Mathematics and Computation, vol. 97, no. 2–3, pp. 139–164, 1998.MathSciNetMATH

[26]

X. P. Li. Partial difference equation used in the study of molecular orbits. Acta Chimica Sinica, vol. 40, no. 8, pp. 688–698, 1982. (in Chinese)

[27]

S. L. Xie, S. S. Cheng. Stability criteria for parabolic type partial difference equations. Journal of Computational and Applied Mathematics, vol. 75, no. 1, pp. 57–66, 1996.MathSciNetCrossRefMATH

[28]

S. S. Cheng, R. Medina. Positive and bounded solutions of discrete reaction-diffusion equations. Applied Mathematics E-Notes, vol. 2, no. 1, pp. 110–116, 2002.MathSciNetMATH

[29]

P. Kachroo, K. Ozbay. Feedback Ramp Metering in Intelligent Transportation Systems, New York, USA: Kluwer Academic/Plenum Publisher, 2003.CrossRef

Titel: Iterative learning control for discrete parabolic distributed parameter systems
verfasst von: Xi-Sheng Dai
Sen-Ping Tian
Ya-Jun Guo
Publikationsdatum: 01.06.2015
Verlag: Institute of Automation, Chinese Academy of Sciences
Erschienen in: Machine Intelligence Research / Ausgabe 3/2015
Print ISSN: 2731-538X
Elektronische ISSN: 2731-5398
DOI: https://doi.org/10.1007/s11633-015-0892-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 3/2015

Nonlinear masking and iterative learning decryption for secure communications

Neural network state learning based adaptive terminal ILC for tracking iteration-varying target points

Repetitive control for TORA benchmark: An additive-state-decomposition-based approach

Lifted system framework for learning control with different trial lengths

Feature selection and feature learning for high-dimensional batch reinforcement learning: A survey

Robust fault-tolerant iterative learning control for discrete systems via linear repetitive processes theory