A Hybrid ISSO-FACS Approach for Optimal Sliding Mode Control of an Inverted Pendulum

Choe, Jin-Hyok; Choe, Gwang; Kwak, Son-Il; Chae, Hyok-Gi; Kong, Hyon-U

doi:10.22111/ijfs.2026.53975.9565

Document Type : Research Paper

Authors

¹ Faculty of Artificial Intelligence, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea

² Faculty of Information Science, Pyongyang University of Computer Science, Pyongyang, Democratic People’s Republic of Korea

https://doi.org/10.22111/ijfs.2026.53975.9565

Abstract

This paper proposes a hybrid approach that integrates an Improved Shark Smell Optimization (ISSO) algorithm with a Fuzzy Ant Colony System (FACS) to enhance the parameter tuning of a fuzzy hierarchical controller for the inverted pendulum and cart system. The standard Shark Smell Optimization (SSO) algorithm suffers from premature convergence and limited exploration capability. The proposed ISSO addresses these limitations by introducing dynamic adaptive coefficients for the gradient and inertia phases, along with a linearly decreasing velocity limit factor. This enhanced global search is then synergistically combined with FACS, which performs fuzzy-guided local exploitation in promising regions of the parameter space. The ISSO-FACS hybrid is applied to determine the optimal sliding surface parameters and scaling factors of a Fuzzy Hierarchical Swing-up and Sliding Controller (FHSSC). Simulation results demonstrate that the proposed approach significantly outperforms the previous FACS method, reducing the total stabilization error by 11.59%, the pendulum angle error by 15.23%, and the cart position error by 26.72%, while achieving 1.27 times faster settling time. The proposed controller also exhibits superior robustness under perturbed initial conditions where the previous method fails, and demonstrates enhanced disturbance rejection capabilities. Convergence analysis confirms the stability properties of the hybrid approach, and computational complexity analysis validates its suitability for offline controller design.

Keywords

Main Subjects

Optimization

References

[1] O. Abedinia, N. Amjady, A. Ghasemi, A new metaheuristic based on shark smell optimization, Complexity, 21(5)
(2014), 97-116. https://doi.org/10.1002/cplx.21634

[2] A. M. A. Amin, M. I. El Korfally, A. A. Sayed, O. T. M. Hegazy, Efficiency optimization of two-asymmetricalwinding
induction motor based on swarm intelligence, IEEE Transactions on Energy Conversion, 24(1) (2009),
12-20. https://doi.org/10.1109/TEC.2008.2011831

[3] G. Andonovski, D. Leite, R. E. Precup, F. Gomide, M. Pratama, I. ˘Skrjanc, Advancements in data-driven evolving
fuzzy and neuro-fuzzy control: A comprehensive survey, Applied Soft Computing, 186 (2026), 114058. https:
//doi.org/10.1016/j.asoc.2025.114058

[4] F. Cuevas, O. Castillo, P. Cortes-Antonio, Optimal design of interval type-2 fuzzy tracking controllers of mobile
robots using a metaheuristic algorithm, in: P. Melin et al. (Eds.), Recent Advances of Hybrid Intelligent Systems
Based on Soft Computing, Studies in Computational Intelligence, 915, Springer, Cham, (2022), 315-341. https:
//doi.org/10.1007/978-3-030-85626-7_62

[5] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE
Transactions on Evolutionary Computation, 6(2) (2002), 182-197. https://doi.org/10.1109/4235.996017

[6] M. Dorigo, M. Birattari, T. St¨utzle, Ant colony optimization, IEEE Computational Intelligence Magazine, 1(4)
(2006), 28-39. https://doi.org/10.1109/MCI.2006.329691

[7] I. Fister, X. S. Yang, I. Fister, J. Brest, D. Fister, A brief review of nature-inspired algorithms for optimization,
Elektrotehniˇski Vestnik, 80(3) (2013), 1-7.

[8] A. H. Gandomi, X. S. Yang, A. H. Alavi, Mixed variable structural optimization using Firefly algorithm, Computers
and Structures, 89(23-24) (2011), 2325-2336. https://doi.org/10.1016/j.compstruc.2011.08.002

[9] Z. W. Geem, J. H. Kim, G. V. Loganathan, A new heuristic optimization algorithm: Harmony search, Simulation:
Transactions of The Society for Modeling and Simulation Internationa, 76(2) (2001), 60-68. https://doi.org/
10.1177/003754970107600201

[10] A. Hentout, A. Maoudj, A. Kouider, Shortest path planning and efficient fuzzy logic control of mobile robots
in indoor static and dynamic environments, Romanian Journal of Information Science and Technology, 2024(1)
(2024), 21-36. https://doi.org/10.59277/ROMJIST.2024.1.02

[11] D. Karaboga, B. Basturk, A powerful and efficient algorithm for numerical function optimization: Artificial bee
colony (ABC) algorithm, Journal of Global Optimization, 39(3) (2007), 459-471. https://doi.org/10.1007/
s10898-007-9149-x

[12] A. Kaveh, T. Bakhshpoori, Water evaporation optimization: A novel physically inspired optimization algorithm,
Computers and Structures, 167 (2016), 69-85. https://doi.org/10.1016/j.compstruc.2016.01.008

[13] J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceedings of the International Conference on Neural
Networks (ICNN 1995), Perth, WA, Australia, Nov. 27-Dec. 1, 4 (1995), 1942-1948. https://doi.org/10.1109/
ICNN.1995.488968

[14] S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Optimization by simulated annealing, Science, 220(4598) (1983), 671-
680. https://doi.org/10.1126/science.220.4598.671

[15] H. J. Kushner, G. G. Yin, Stochastic approximation and recursive algorithms and applications, 2nd ed. Springer,
2003. https://doi.org/https://doi.org/10.1007/b97441

[16] Q. Lin, S. Wu, S. Wu, H. Wang, J. Zhang, Development and simulation of two novel indoor odor source localization
methods using a modified shark smell optimization algorithm, Measurement, 240 (2025), 115562. https://doi.
org/10.1016/j.measurement.2024.115562

[17] S. Mirjalili, The ant lion optimizer, Advances in Engineering Software, 83 (2015), 80-98. https://doi.org/10.
1016/j.advengsoft.2015.01.010

[18] S. Mirjalili, A. Lewis, S-shaped and V-shaped transfer functions for binary particle swarm optimization, Swarm
and Evolutionary Computation, 9 (2013), 1-14. https://doi.org/10.1016/j.swevo.2012.09.002

[19] S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey wolf optimizer, Advances in Engineering Software, 69 (2014), 46-61.
https://doi.org/10.1016/j.advengsoft.2013.12.007

[20] S. Mirjalili, S. Saremi, S. M. Mirjalili, L. dos S. Coelho, Multi-objective grey wolf optimizer: A novel algorithm for
multi-criterion optimization, Expert Systems with Applications, 47 (2016), 106-119. https://doi.org/10.1016/
j.eswa.2015.10.039

[21] M. M. Noel, A new gradient based particle swarm optimization algorithm for accurate computation of global minimum, Applied Soft Computing, 12(1) (2012), 353-359. https://doi.org/10.1016/j.asoc.2011.08.037

[22] R. E. Precup, C. A. Bojan-Dragos, K. Gao, Problem setting for trajectory planning and cruise control of a connected
autonomous electric bus in intersection scenarios with human-driven vehicles to optimize energy, comfort and
tracking, Romanian Journal of Information Science and Technology, 28(3) (2025), 299-312. https://doi.org/10.
59277/ROMJIST.2025.3.05

[23] R. E. Precup, R. C. Roman, E. M. Hedrea, C. A. Szedlak-Stinean, I. A. Zamfirache, Classical and modern optimization
techniques applied to control and modeling, Boca Raton, FL: CRC Press, 2025. https://doi.org/10.
1201/9781003488279

[24] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA: A gravitational search algorithm, Information Sciences,
179(13) (2009), 2232-2248. https://doi.org/10.1016/j.ins.2009.03.004

[25] A. Seifi, M. Ehteram, F. Soroush, Uncertainties of instantaneous influent flow predictions by intelligence models
hybridized with multi-objective shark smell optimization algorithm, Journal of Hydrology, 587 (2020), 124977.
https://doi.org/10.1016/j.jhydrol.2020.124977

[26] R. Storn, K. Price, Differential evolution - a simple and efficient heuristic for global optimization over continuous
spaces, Journal of Global Optimization, 11(4) (1997), 341-359. https://doi.org/10.1023/A:1008202821328

[27] C. W. Tao, J. S. Taur, C. M. Wang, U. S. Chen, Fuzzy hierarchical swing-up and sliding position controller for the
inverted pendulum-cart system, Fuzzy Sets and Systems, 159(20) (2008), 2763-2784. https://doi.org/10.1016/
j.fss.2008.02.005

[28] G. G. Wang, L. Guo, A. H. Gandomi, G. S. Hao, H. Wang, Chaotic Krill Herd algorithm, Information Sciences,
274 (2014), 17-34. https://doi.org/10.1016/j.ins.2014.02.123

[29] X. S. Yang, Firefly algorithm, stochastic test functions and design optimisation, International Journal of Bio-
Inspired Computation, 2(2) (2010), 78-84. https://doi.org/10.1504/IJBIC.2010.032124

Iranian Journal of Fuzzy Systems

A Hybrid ISSO-FACS Approach for Optimal Sliding Mode Control of an Inverted Pendulum

References

References

Volume 23, Issue 3
May and June 2026
Pages 51-68

A Hybrid ISSO-FACS Approach for Optimal Sliding Mode Control of an Inverted Pendulum

References

References

Volume 23, Issue 3May and June 2026Pages 51-68

Volume 23, Issue 3
May and June 2026
Pages 51-68