---

Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 303--314 | DOI:10.5890/DNC.2025.06.005

Smita Sonker$^{1,2}$, Neeraj Devi$^{1}$

$^1$ Department of Mathematics, National Institute of Technology Kurukshetra, Kurukshetra-136119, India

$^2$ School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India

Download Full Text PDF

 

Abstract

In this study, we proposed a method for the pole optimization of the linear Muti Input Multi Output (MIMO)-Laguerre model using artificial bee colonies. The independent and orthonormal Laguerre basis is used to expand the system's inputs and outputs. The artificial bee colony (ABC) technique is used to model MIMO-Laguerre systems and the results are studied. Using this approach, the model parameters for the systems are generated and the algorithm's performance is compared with genetic algorithm and training functions. A numerical simulation to the CSTR Benchmark validates the optimization of Laguerre poles.

References

1. [1]	Borghi, G., Herty, M., and Pareschi, L. (2023), An adaptive consensus based method for multi-objective optimization with uniform pareto front approximation, Applied Mathematics and Optimization, 88(2), 1-43.

2. [2]	Fu, Y. and Dumont, G.A. (1993), An optimum time scale for discrete Laguerre network, IEEE Transactions on Automatic Control, 38(6), 934-938.

3. [3]	de Silva, T.O. (1995), On the determination of the optimal pole position of laguerre filter, IEEE Transactions on Signal Processing, 43(9), 2079-2087.

4. [4]	Tanguy, N., Morvan, R., Vilbé, P., and Calvez, L.C. (2000), Online optimization of the time scale in adaptive Laguerre-based filters, IEEE Transactions on Signal Processing, 48(4), 1184-1187.

5. [5]	Ngia, L.S. (2001), Separable nonlinear least-squares methods for efficient off-line and on-line modeling of systems using Kautz and Laguerre filters, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 48(6) , 562-579.

6. [6]	Garna, T., Bouzrara, K., Ragot, J., and Messaoud, H. (2013), Nonlinear system modeling based on bilinear Laguerre orthonormal bases, ISA Transactions, 52(3), 301-317.

7. [7]	Malti, R., Ekongolo, S.B., and Ragot, J. (1998), Dynamic SISO and MISO system approximations based on optimal Laguerre models, IEEE transactions on Automatic Control, 43(9), 1318-1323.

8. [8]	Ninness, B. and Gustafsson, F. (1997), A unifying construction of orthonormal bases for system identification, IEEE Transactions on Automatic Control, 42(4), 515-521.

9. [9]	Wahlberg, B. (1994), System identification using Kautz models, IEEE Transactions on Automatic Control, 39(6), 1276-1282.

10. [10]	Bouzrara, K., Garna, T., Ragot, J., and Messaoud, H. (2012), Decomposition of an ARX model on Laguerre orthonormal bases, ISA Transactions, 51(6), 848-860.

11. [11]	El Anes, A., Maraoui, S., and Bouzrara, K. (2017), Gradient method for optimal expansions of MIMO ARX model on Laguerre bases, In 2017 International Conference on Control, Automation and Diagnosis (ICCAD), IEEE, 007-012.

12. [12]	Yousfi, M., Garna, T., and Njima, C.B. (2020), Poles optimization of MIMO ARX-Laguerre model using genetic algorithm, International Journal of Applied Mathematics, Computational Science and Systems Engineering, 2.

13. [13]	Chaudhary, K.S. and Kumar, N. (2023), Fractional order fast terminal sliding mode control scheme for tracking control of robot manipulators, ISA Transactions, 142(2023), 57-69.

14. [14]

    Karaboga, D. and Basturk, B. (2007), Artificial bee colony (ABC) optimization algorithm for solving constrained optimization problems, In Foundations of Fuzzy Logic and Soft Computing: 12th International Fuzzy Systems Association World Congress, IFSA 2007, Cancun, Mexico, June 18-21, Springer Berlin Heidelberg, Proceedings 12, 789-798.

15. [15]	Karaboga, D. (2005), An Idea based on Honey Bee Swarm for Numerical Optimization, Technical report-tr06, Erciyes university, engineering faculty, computer engineering department, 200, 1-10.

16. [16]	Demuth, H., Beale, M., and Hagan, M. (2000), Neural Network Toolbox, For Use with MATLAB, The MathWorks Inc 1992.