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Iterative Learning Control Design Based on State Observer

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Abstract

Linear control systems operating in a repetitive mode with a constant period and returning each time to the initial state are considered. The problem is to find a control law that will employ information about the output variable at the current and previous repetitions and also the estimates of state variables from an observer in order to guarantee the convergence of this variable to a reference trajectory under unlimited increasing the repetitions number. This type of control is known as iterative learning control. The problem is solved using the dissipativity of 2D models and the divergent method of vector Lyapunov functions. The final results are expressed in the form of linear matrix inequalities. An example is given.

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References

  1. Bristow, D.A., Tharayil, M., and Alleyne, A.G., A Survey of Iterative Learning Control, IEEE Control Syst. Magazine, 2006, vol. 23, no. 3, pp. 96–114.

    Google Scholar 

  2. Ahn, H.-S., Chen, Y.Q., and Moore, K.L., Iterative Learning Control: Brief Survey and Categorization, IEEE Trans. Syst., Man, Cybernet., Part C: Applications and Reviews, 2007, vol. 37, no. 6, pp. 1099–1121.

    Article  Google Scholar 

  3. Ahn, H.-S., Moore, K.L., and Chen, Y.Q., Iterative Learning Control. Robustness and Monotonic Convergence for Interval Systems, London: Springer-Verlag, 2007.

    MATH  Google Scholar 

  4. Arimoto, S., Kawamura, S., and Miyazaki, F., Bettering Operation of Dynamic Systems by Learning: A New Control Theory for Servomechanism or Mechatronic Systems, Proc. 23rd Conf. Decision Control, Las Vegas, 1984, pp. 1064–1069.

    Google Scholar 

  5. Arimoto, S., Kawamura, S., and Miyazaki, F., Bettering Operation of Robots by Learning, J. Robot. Syst., 1984, vol. 1, no. 2, pp. 123–140.

    Article  Google Scholar 

  6. Hladowski, L., Galkowski, K., Cai, Z., Rogers, E., Freeman, C., and Lewin, P., Experimentally Supported 2D Systems Based Iterative Learning Control Law Design for Error Convergence and Performance, Control Eng. Pract., 2010, vol. 18, pp. 339–348.

    Article  Google Scholar 

  7. Shen, D. and Wang, Y., Survey on Stochastic Iterative Learning Control, J. Process Control, 2014, vol. 24, pp. 64–77.

    Article  Google Scholar 

  8. Shen, D., A Technical Overview of Recent Progresses on Stochastic Iterative Learning Control, Unmanned Syst., 2018, vol. 6, no. 3, pp. 147–164.

    Article  Google Scholar 

  9. Jayawardhana, R.N. and Ghosh, B.K., Observer Based Iterative Learning Controller Design for MIMO Systems in Discrete Time, Proc. 2018 Ann. Am. Control Conf. (ACC), Milwaukee, 2018, pp. 6402–6408.

    Chapter  Google Scholar 

  10. Jayawardhana, R.N. and Ghosh, B.K., Kalman Filter Based Iterative Learning Control for Discrete Time MIMO Systems, Proc. 30th Chinese Control and Decision Conf. (2018 CCDC), Shenyang, 2018, pp. 2257–2264.

    Google Scholar 

  11. Saab, S.S., A Discrete-Time Stochastic Learning Control Algorithm, IEEE Trans. Autom. Control, 2001, vol. 46, pp. 877–887.

    Article  MathSciNet  Google Scholar 

  12. Paszke, W., Rogers, E., and Patan, K., Observer-Based Iterative Learning Control Design in the Repetitive Process Setting, IFAC-PapersOnline, 2017, vol. 50, no. 1, pp. 13390–13395.

    Article  Google Scholar 

  13. Rogers, E., Galkowski, K., and Owens, D.H., Control Systems Theory and Applications for Linear Repetitive Processes, Lect. Notes Control Inform. Sci., vol. 349, Berlin: Springer-Verlag, 2007.

    MATH  Google Scholar 

  14. Pakshin, P., Emelianova, J., Emelianov, M., Galkowski, K., and Rogers, E., Dissipivity and Stabilization of Nonlinear Repetitive Processes, Syst. Control Lett., 2016, vol. 91, pp. 14–20.

    Article  Google Scholar 

  15. Galkowski, K., Emelianov, M., Pakshin, P., and Rogers, E., Vector Lyapunov Functions for Stability and Stabilization of Differential Repetitive Processes, J. Comput. Syst. Sci. Int., 2016, vol. 55, pp. 503–514.

    Article  MathSciNet  Google Scholar 

  16. Goldsmith, P.B., On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control, Automatica, 2002, vol. 38, no. 4, pp. 703–708.

    Article  MathSciNet  Google Scholar 

  17. Goldsmith, P.B., Author's reply to “On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control,” Automatica, 2004, vol. 40, no. 5, pp. 899–900.

    Article  MathSciNet  Google Scholar 

  18. Owens, D.H. and Rogers, E., Comments on “On the Equivalence of Causal LTI Iterative Learning Control and Feedback Control,” Automatica, 2004, vol. 40, no. 5, pp. 895–898.

    Article  MathSciNet  Google Scholar 

  19. Willems, J.C., Dissipative Dynamical Systems. Part I: General Theory, Arch. Ration. Mech. Anal., 1972, vol. 45, pp. 321–351.

    Article  Google Scholar 

  20. Byrnes, C.I., Isidori, A., and Willems, J.C., Passivity, Feedback Equivalence and the Global Stabilization of Minimun Phase Nonlinear Systems, IEEE Trans. Autom. Control, 1991, vol. 36, pp. 1228–1240.

    Article  Google Scholar 

  21. Fradkov, A.L. and Hill, D.J., Exponential Feedback Passivity and Stabilizability of Nonlinear Systems, Automatica, 1998, vol. 34, pp. 697–703.

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the Russian Science Foundation, project no. 18-79-00088.

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Authors and Affiliations

  1. Arzamas Polytechnic Institute of R.E. Alekseev Nizhny Novgorod State Technical University, Arzamas, Russia

    J. P. Emelianova & P. V. Pakshin

Authors
  1. J. P. Emelianova
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  2. P. V. Pakshin
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Correspondence to J. P. Emelianova or P. V. Pakshin.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 9, pp. 9–24.

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Emelianova, J.P., Pakshin, P.V. Iterative Learning Control Design Based on State Observer. Autom Remote Control 80, 1561–1573 (2019). https://doi.org/10.1134/S0005117919090017

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