Vol. 21 No. 2 (2022): Revista UIS Ingenierías
Articles

Optimal state estimator in discrete time

Fernando Mesa
Universidad Tecnológica de Pereira
Rogelio Ospina
Universidad Industrial de Santander

Published 2022-03-15

Keywords

  • quadratic control,
  • Objective Function,
  • optimization

How to Cite

Mesa, F., Ospina, R. ., & Correa-Vélez , G. . (2022). Optimal state estimator in discrete time. Revista UIS Ingenierías, 21(2), 15–20. https://doi.org/10.18273/revuin.v21n2-2022002

Abstract

A study of state estimation was performed on models with noise in control systems considering the observer design and the state feedback. For this purpose, noise on the state space model of the system was considered, and the best possible observer was designed: that is to say, the one that better rejects the noise effect. These observers are usually called estimators. In this work an estimator known as the Kalman filter was developed.

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References

  1. A. Dávila Gómez, A. Peña Palacio, P. A. Ortiz Valencia, E. Delgado Trejos, “Dinámica Estocástica o Compleja con Información Incompleta: Una Revisión desde el Control”, Iteckne, vol.10 no.1, pp. 113-127, 2013, doi: https://doi.org/10.15332/iteckne.v10i1.186
  2. D. González Montoya, P. A. Ortiz Valencia, C. A. Ramos-Paja, “Fixed-frequency implementation of sliding-mode controllers for photovoltaic systems”, International Journal of Energy and Environmental Engineering, vol. 10, pp. 287–305, 2019, doi: https://doi.org/10.1007/s40095-019-0306-z
  3. M. M. Seron, J. H. Braslavsky, G.C. Goodwin, Fundamental limitations in filtering and control. Callaghan, Australia: Springer, 2007, doi: https://doi.org/10.1007/978-1-4471-0965-5
  4. X. Wang, “Solving optimal control problems with MATLAB: Indirect methods”, Ncsu.Edu., 2015.
  5. H. Purnawan, E. B. Purwanto, “Design of linear quadratic regulator (LQR) control system for flight stability of LSU-05”, Journal of Physics: Conference Series, vol. 890, no. 1, pp. 1-6, 2017, doi: https://doi.org/10.1088/1742-6596/890/1/012056
  6. G. C. Goodwin, K. S. Sin, “Adaptive filtering prediction and control”, Courier Corporation, Dover Publications, New York, 2014.
  7. N. Safari-Shad, N. Abedi, S. Dehsarvi, “Nonlinear optimal control design experiments using the inverted pendulum on a cart paradigm”, European Control Conference (ECC), Karlsruhe, pp. 197-202, 1999, doi: https://doi.org/10.23919/ECC.1999.7099299
  8. M. Athans, P. L. Falb, Optimal control: an introduction to the theory and its applications. New York, USA: Dover Publications, 2007.
  9. T. Basar, P. Bernhard, H∞ Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. New York, USA: Springer, 2008.
  10. R. G. Brown, P.Y. Hwang, Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises. New York, USA: Wiley, 2012.
  11. W. Wang, C. Han, X. Wang, “Optimal Estimation for Continuous-Time Stochastic systems with Delayed measurements and Multiplicative noise,” 2020 IEEE 16th International Conference on Control & Automation (ICCA), 2020, pp. 961-966, doi: https://doi.org/10.1109/ICCA51439.2020.9264532
  12. L. Pogorelyuk, C. W. Rowley, N. J., Kasdin, “An efficient approximation of the Kalman filter for multiple systems coupled via low-dimensional stochastic input”, Automatica, vol. 117, 2020, doi: https://doi.org/10.1016/j.automatica.2020.108972
  13. S. Zhou, G. Feng, “H∞ Filtering for Discrete-time Systems with Randomly Varying Sensor Delays”, Automatica, vol. 44, no. 7, pp. 1918- 1922, 2008, doi: https://doi.org/10.1016/j.automatica.2007.10.026
  14. J. T. Monserrat, “Allocation of flow to plots in pressurized irrigation distribution networks: Analysis of the Clement and Galand method and a new proposal”, Journal of Irrigation and Drainage Engineering, vol. 135, pp. 1-6. 2009, doi: https://doi.org/10.1061/(ASCE)0733-9437(2009)135:1(1)
  15. K. Ogata, Dinámica de sistemas. Prentice Hall Hispanoamericana, México, 1987.
  16. R. C. Dorf, R. H. Bishop, “Modern control systems twelfth edition,” Pearson, 2011.
  17. A. C. Harvey, “Forecasting, Structural Time Series Models and the Kalman Filter”, Cambridge University Press, London, 2014. doi: https://doi.org/10.1017/CBO9781107049994
  18. H. Zhang, G. Feng, C. Han, “Linear estimation for random delay systems,” Systems & Control Letters, vol. 60, no. 2, pp. 450-459, 2011, doi: https://doi.org/10.1016/j.sysconle.2011.03.009