Intelligent maximum likelihood self-adjustable block roots assignment for a class of MIMO stochastic systems

Belkacem Bekhiti; George F. Fragulis; Kamel Hariche

doi:10.2478/candc-2025-0014

.blurhash-client-img { display: none !important; }

Intelligent maximum likelihood self-adjustable block roots assignment for a class of MIMO stochastic systems

Control and Cybernetics

Volume 54 (2025): Issue 4 (December 2025)

By: Belkacem Bekhiti, George F. Fragulis and Kamel Hariche

Open Access

|Mar 2026

Abstract

This paper presents a new self-adjustable block roots assignment control scheme for multivariable stochastic systems, via the use of conventional intelligent MIMO maximum likelihood identification algorithm, handled with an adaptive neural based fuzzy inference system (ANFIS). The proposed state-space self-tuning control methodology can be applied to the multivariable stochastic system without requiring prior knowledge of system parameters and noise properties. Illustrative examples demonstrate the effectiveness of the proposed approach.

References

Agüero, J. C., Yuz, J. I., Goodwin, G. C. and Delgado, R. A. (2010) On the equivalence of time and frequency domain maximum likelihood estimation. Automatica, 46 (2) 260–270.
Search in Google Scholar Back to article
Ahmed, S., Huang, B. and Shah, S. L. (2007) Novel identification method from step response. Control Engineering Practice, 15 (5) 545–556.
Search in Google Scholar Back to article
Akroum, M. and Hariche, K. (2008) An optimal instrumental variable identification method for LMFD models, Studies in Informatics and Control, 17, 4.
Search in Google Scholar Back to article
Akroum, M. and Hariche K. (2009) Extending the SRIV algorithm to LMFD models, Journal of Electrical Engineering and Technology, Korean Institute of Electrical Engineers, 4, 1.
Search in Google Scholar Back to article
Akroum, M. and Hariche K. (2010) Right matrix fraction description models identification using constrained PEM. Kuwait J. Sci. & Eng. 37 (1B) 69-88.
Search in Google Scholar Back to article
Åström, K. J. and Wittenmark, B. (1989) Adaptive Control. Addison-Wesley, New York.
Search in Google Scholar Back to article
Bao, B., Xu, Y.-q., Sheng, J. and Ding, R.-f. (2011) Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data. Mathematical and Computer Modelling, 53, 1664–1669.
Search in Google Scholar Back to article
Barbosa, G. C. and Silvestre, F. J. (2025) Output feedback fuzzy gain scheduling for MIMO systems applied to flexible aircraft control. Aerospace, 12, 6, 557. doi: 10.3390/aerospace12060557
Search in Google Scholar Back to article
Bekhiti, B. (2015) On the theory of λ-matrices based MIMO control system design. Control and Cybernetics 44, 4.
Search in Google Scholar Back to article
Bekhiti, B. (2018) Multivariable control system design using the theory of matrix polynomials. Ph.D. dissertation. Univ. M’Hamed Bougara-Boumerdes, Algeria.
Search in Google Scholar Back to article
Bekhiti, B. (2020a) On the order reduction of MIMO large-scale systems using block-roots of matrix polynomials. Int. J. Comput. Appl. Eng. Technol., 12, 2, 157–181, doi: 10.1504/IJCAET.2020.105576
Search in Google Scholar Back to article
Bekhiti, B. (2020b) On the block decomposition and spectral factors of λ-matrices. Control and Cybernetics, 49, 1, 41–76.
Search in Google Scholar Back to article
Bekhiti, B. (2024) Advanced Strategies for Guidance & Control of SAM Missiles. Lambert Academic Publishing, Saarbruecken, Germany.
Search in Google Scholar Back to article
Bekhiti, B. (2025) Neural adaptive nonlinear MIMO control for bipedal walking robot locomotion in hazardous and complex task applications. Robotics, 14, 6, 84. doi: 10.3390/robotics14060084
Search in Google Scholar Back to article
Bekhiti, B., Dahimene, A., Nail, B. and Hariche, K. (2015) On Block Roots of Matrix Polynomials Based MIMO Control System Design. 4 ^th International Conference on Electrical Engineering ICEE Boumerdes.
Search in Google Scholar Back to article
Bekhiti, B., Fragulis, G. F., Rahmouni, M. and Hariche, K. (2025a) A novel threedimensional sliding pursuit guidance and control of surface-toair missiles. Technologies, 13, 5, 171. doi: 10.3390/technologies13050171
Search in Google Scholar Back to article
Bekhiti, B., Nail, B., Tibermacine, I. E. and Salim, R. (2025b) On hyper-stability theory based multivariable nonlinear adaptive control: Experimental validation on induction motors. IET Electr. Power Appl., 19, 1, Jan. 2025. doi: 10.1049/elp2.70035
Search in Google Scholar Back to article
Dahimene, A. (2009) Incomplete matrix partial fraction expansion. Control and Cybernetics 38, 3.
Search in Google Scholar Back to article
Dennis, J. E., Traub, J. F. and Weber, R. P. (1976) The algebraic theory of matrix polynomials. SIAM J. Numer. Anal., 13: 831-845.
Search in Google Scholar Back to article
Dennis, J. E., Traub, J. F. and Weber, R. P. (1978) Algorithms for solvents of matrix polynomials. SIAM J. Numer. Anal., 15:523-533.
Search in Google Scholar Back to article
Gao, J. (2023) Output feedback based poles configuration for LDP systems with varying state and input dimensions. IET Control Theory Appl., 17, 318–330.
Search in Google Scholar Back to article
Gohberg, I., Kaashoek, M. A. and Rodman, L. (1978) Spectral analysis of families of operator polynomial and a generalized Vandermonde matrix,1. The finite dimensional case. In: Topics in Functional Analysis: Essays Dedicated to M. G. Krein on the Occasion of His 70^th Birthday. Academic Press, New York, 91-128.
Search in Google Scholar Back to article
Gohberg, I., Lancaster, P. and Rodman, L. (1982) Matrix Polynomials. Academic Press.
Search in Google Scholar Back to article
Guo, Sh.-M., Shieh, L. S. and Coleman, N. P. (2001) Observer-Type Kalman Innovation Filter for Uncertain Linear Systems. IEEE Transactions On Aerospace And Electronic Systems, 37, 4, 1406–1418.
Search in Google Scholar Back to article
Guo, Sh.-g., Zhu, F.-l. and Xu, L.-y. (2015) Unknown Input Observer Design for Takagi-Sugeno Fuzzy Stochastic System. International Journal of Control, Automation, and Systems 13(4):1003-1009.
Search in Google Scholar Back to article
Hariche, K. (1987) Interpolation Theory in the Structural Analysis of λ-matrices: Chapter 3, Ph. D. Dissertation, University of Houston.
Search in Google Scholar Back to article
Hassan, M. F., Alrifai, M. T., Soliman, H. M. and Kourah, M. A. (2015) Observer-based controller for constrained uncertain stochastic nonlinear discrete-time systems. Int. J. Robust Nonlinear Control, 26, 10, 2090–2115.
Search in Google Scholar Back to article
He, N. (2020) Analytical tuning method of MPC controllers for MIMO first-order plus fractional dead time systems. Processes, 8, 2, 212. doi: 10.3390/pr8020212
Search in Google Scholar Back to article
Hendricks, E., Jannerup, O. and Sorensen, P. H. (2008) Linear Systems Control. Deterministic and Stochastic Methods. Springer-Verlag, Berlin-Heidelberg.
Search in Google Scholar Back to article
Jang, J.-S. R. (1993) ANFIS: Adaptive-Network-based Fuzzy Inference System. IEEE Trans. on Systems, Man, and Cybernetics, 23:665-685.
Search in Google Scholar Back to article
Kalman, R. E. (1963) Mathematical Description of Linear Systems. SIAM J. Control, 1, 152-192.
Search in Google Scholar Back to article
Kalman, R. E., Falb, R. L. and Arbib, M. A. (1969) Topics in Mathematical System Theory. McGraw-Hill, New York.
Search in Google Scholar Back to article
Liu, Y. and Zhu, Q. (2021) Adaptive neural network asymptotic tracking control for non-strict feedback stochastic nonlinear systems. Neural Networks, 143, 283–290.
Search in Google Scholar Back to article
Liu, Y. J., Sheng, J. and Ding, R. F. (2010) Convergence of stochastic gradient algorithm for multivariable ARX-like systems. Computers & Mathematics with Applications, 59 (8) 2615–2627.
Search in Google Scholar Back to article
Ljung, L. (1999) System Identification: Theory for the User. Prentice-Hall, Englewood Cliffs, NJ.
Search in Google Scholar Back to article
Mohamed, M. and Kar, I. N. (2015) Stochastic contraction-based observer and controller design algorithm with application to a flight vehicle. International Journal of Control, 88, 11.
Search in Google Scholar Back to article
Pan, J. (2023) From nonlinear dominant system to linear dominant system: Virtual equivalent system approach for multiple variable self-tuning control system analysis. Entropy, 25, 1, 173. doi: 10.3390/e25010173
Search in Google Scholar Back to article
Pereira, E. (2003) Block eigenvalues and solution of differential matrix equation. Miskolc Mathematical Notes, 4, 1, 45-51.
Search in Google Scholar Back to article
Rahimi Mousavi, M. S. and Boulet, B. (2016) Estimation of the State Variables and Unknown Input of a Two-Speed Electric Vehicle Driveline Using Fading-Memory Kalman Filter. IEEE Transactions on Transportation Electrification, 2, 2, 210–220, June 2016.
Search in Google Scholar Back to article
Razavi, H., Merat, K., Salarieh, H., Alasty, A. and Meghdari, A. (2016) Observer based minimum variance control of uncertain piecewise affine systems subject to additive noise, Nonlinear Analysis: Hybrid Systems 19 153–167.
Search in Google Scholar Back to article
Schröders, S. (2020) Two-degree-of-freedom MIMO control for hydraulic servosystems with switching properties. Control Eng. Pract., 95, 104246.
Search in Google Scholar Back to article
Shieh, L. S., Bao, Y. L. and Chang, F. R. (1989) State-space self-tuning regulators for general multivariable stochastic systems. IEE Proceedings D: Control Theory and Applications, 136, 1, 17–27.
Search in Google Scholar Back to article
Shieh, L. S., Chang, F.-R. and McInnis, B. C. (1986) The block partial fraction expansion of a matrix fraction description with repeated block poles. IEEE Trans. Automat. Control, 31:23-36.
Search in Google Scholar Back to article
Shieh, L. S. and Tsay, Y. T. (1981) Transformation of solvent and spectral factors of matrix polynomial, and their applications. Internat. J. Control 34:813-823.
Search in Google Scholar Back to article
Shieh, L. S. and Tsay, Y. T. (1982a) Block modal matrices and their applications to multivariable control systems. IEE Proc. D Control Theory Appl., 2:41-48.
Search in Google Scholar Back to article
Shieh, L. S. and Tsay, Y. T. (1982b) Transformation of a class of multivariable control systems to block companion forms. IEEE Trans. Automat. Control 27: 199-203.
Search in Google Scholar Back to article
Stevens, B. L. and Lewis, F. L. (2003) Aircraft Control and Simulation, 2nd ed. Wiley-Interscience, New York.
Search in Google Scholar Back to article
Trojaola, I. (2021) An innovative MIMO iterative learning control approach for the position control of a hydraulic press. IEEE Access, 9, 146850–146867.
Search in Google Scholar Back to article
Tsay, Y. T. and Shieh, L. S. (1981) State-space approach for self-tuning feedback control with pole assignment. IEE Proc. D, Control Theory Appl. 123, 93–101.
Search in Google Scholar Back to article
Warwick, K. (1981) Self-tuning regulators –a state-space approach. Int. J. Control, 33, 839–858.
Search in Google Scholar Back to article
Wu, C.-Y., Tsai, j. S.-H., Guo, S.-M., Shieh, L.-S., Canelon, J. I., Ebrahimzadeh, F. and Wang, L. A. (2014) Novel on-line observer/Kalman filter identification method and its application to input-constrained active faulttolerant tracker design for unknown stochastic systems, systems. Journal of the Franklin Institute, 352, 3, 1119–1151, March 2015.
Search in Google Scholar Back to article
Yaici, M. and Hariche, K. (2014) On eigenstructure assignment using block poles placement, European Journal of Control, 20, 5, 217–226, September 2014.
Search in Google Scholar Back to article
Yaici, M., Hariche, K. and Clark, T. (2014) A Contribution to the Polynomial Eigen Problem, International Journal of Mathematics, Computational, Natural and Physical Engineering, 8, 10.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/candc-2025-0014 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569

Journal RSS Feed

Language: English

Page range: 389 - 419

Submitted on: Feb 1, 2025

Accepted on: Dec 1, 2025

Published on: Mar 9, 2026

Published by: Systems Research Institute Polish Academy of Sciences

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

solvents,

self-adjustable block roots,

Related subjects:

Computer sciences, other,

Engineering,

Electrical engineering,

Fundamentals of electrical engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Mathematics,

General mathematics

© 2026 Belkacem Bekhiti, George F. Fragulis, Kamel Hariche, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 54 (2025): Issue 4 (December 2025)