Paper:

# Optimization of Fuzzy Logic Controller for Trajectory Tracking Using Genetic Algorithm

## Pintu Chandra Shill^{*}, M. A. H. Akhand^{**},

Md. Faijul Amin^{*}, and Kazuyuki Murase^{*}

^{*}Department of System Design Engineering, Graduate School of Engineering, University of Fukui, 3-9-1 Bunkyo, Fukui 910-8507, Japan

^{**}Department of Computer Science and Engineering (CSE), Khulna University of Engineering & Technology (KUET), Khulna 9203, Bangladesh

Most Fuzzy Logic Controllers (FLCs) to date are working based on expert knowledge derived from heuristic knowledge of experienced operators. Conventional fuzzy logic controllers have poor adaptability due to invariable Membership Function (MF) parameters and fixed rule set. Conventional manual coded FLCs use only expert knowledge bases and do poorly with complex problems, especially with large numbers of input variables. We have developed FLCs using a Genetic Algorithm (GA) to automatically acquire knowledge that we call a genetic-fuzzy in which the GA is used to adaptively generate fuzzy rules and simultaneously selecting an appropriate MF shape. We also evaluate different membership functions in the fuzzy logic control. FLC sensibility is analysed and compared for different membership functions. We compare our proposed genetic-fuzzy approach to such existing methods, including as a manually coded conventional method, conventional method with complementary membership function, and a neuro-fuzzy method on a widely used test bed; backing up a truck reversal problem. Simulation results have shown our proposal to be superior to existing widely used methods.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.15, No.6, pp. 639-651, 2011.

- [1] A. Bagis, “Fuzzy and PD controller based intelligent control of spillway gates of dams,” Intelligent Fuzzy Systems, Vol.14, No.1, pp. 25-36, 2003.
- [2] L. X.Wang, “Adaptive fuzzy systems and control design and stability analysis,” Prentice Hall, 1994.
- [3] K. Belarbi, F. Titel, W. Bourebia, and K. Benmahammed, “Design of Mamdani fuzzy logic controllers with rule base minimisation using genetic algorithm,” J. of Engineering Applications of Artificial Intelligence, Vol.18, pp. 875-880, 2005.
- [4] A. Arslan and M. Kaya, “Determination of fuzzy logic membership functions using genetic algorithms,” Fuzzy Sets and Systems, Vol.118, pp. 297-306, 2001.
- [5] D. L. Meredith, C. L. Karr, and K. Krishna Kumar, “The use of genetic algorithms in the design of fuzzy logic controllers,” Proc. of Third Workshop on Neural Networks: Academic/Industrial/Defence (WNN’92), pp. 1105-1109, 1992.
- [6] A. Bagis, “Fuzzy rule base design using tabu search algorithm for nonlinear system modeling,” ISA Trans., Vol.47, pp. 32-44, 2008.
- [7] Y. Li and Y. Li, “Neural-fuzzy control of truck backer-upper system using a clustering method,” Neuro Computing, Vol.70, pp. 680-688, 2007.
- [8] C. C. Yang and N. K. Bose, “Generating fuzzy membership function with self-organizing feature map,” Pattern Recognition Letters, Vol.27, pp. 356-365, 2006.
- [9] A. F. M. Huang, S. J . H. Yang, M. Wang, and J. J. P. Tsai, “Improving fuzzy knowledge integration with particle swarm optimization,” Expert Systems with Applications, Vol.37, pp. 8770-8783, 2010.
- [10] S. E. Papadakis and J. B. Theocharis, “A GA-based fuzzy modeling approach for generating TSK models,” Fuzzy Sets and Systems, Vol.131, No.2, pp. 121-152, 2002.
- [11] M. Russo, “Genetic Fuzzy Learning,” IEEE Trans. on Evolutionary Computation, Vol.4, No.3, pp. 259-273, 2000.
- [12] F. Herrera and M. Lozano, “Adaptive genetic operators based on coevolution with fuzzy behaviors,” IEEE Trans. on Evolutionary Computation, Vol.5, No.2, pp. 149-165, 2001.
- [13] Y. Shi, R. Eberhart, and Y. Chen, “Implementation of evolutionary fuzzy systems,” IEEE Trans. on Fuzzy Systems, Vol.7, pp. 109-119, 1999.
- [14] N. B. Hui and D. K. Pratihar, “Automatic design of fuzzy logic controller using a genetic algorithm for collision-free, time-optimal navigation of a car-like robot,” Int. J. of Hybrid Intelligent Systems, Vol.2, No.3, pp. 161-187, 2005.
- [15] F. Herrera, M. Lozano, and J. L. Verdegay, “A learning process for fuzzy control rules using genetic algorithms,” Fuzzy Sets and Systems, Vol.100, pp. 143-158, 1998.
- [16] C. L. Karr, “Design of an adaptive fuzzy logic controller using a genetic algorithm,” Proc. of 4th Int. Conf. on Genetic Algorithms, pp. 450-457, 1991.
- [17] S. Bai and S. Chen, “Automatically constructing grade membership functions of fuzzy rules for students’ evaluation,” Expert Systems with Applications, Vol.35, pp. 1408-1414, 2008.
- [18] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol.8, pp. 338-353, 1965.
- [19] D. G. Burkhardt and P. P. Bonissone, “Automated fuzzy knowledge base Generation and tuning,” Proc. of IEEE Int. Conf. on Fuzzy Systems, pp. 179-188, 1992.
- [20] B. Kosko, “Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence,” Prentice Hall, 1992.
- [21] T. Koga, K. Horio, and T. Yamakawa, “Self-organizing Relationship (SOR) Network with fuzzy Inference Based Evaluation and Its application to Trailer-Truck Back-up control,” Proc. of 11th Int. Conf. on Neural Information Processing (ICONIP), pp. 368-374, 2004.
- [22] M. Mohammadian and R. J. Stonier, “Generating fuzzy rules by genetic algorithms,” Proc. of 3rd Int. workshop on Robot and Human Communication, Nagoya, Japan, pp. 362-367, 1994.
- [23] K. Belarbi, F. Titel, W. Bourebia, and K. Benmahammed, “Design of Mamdani fuzzy logic controllers with rule base minimisation using genetic algorithm,” Engineering Applications of Artificial Intelligence, Vol.18, No.7, pp. 875-880, 2005.
- [24] H. J. Zimmermann, “Fuzzy Set Theory and its Application,” 2nd edition, Allied Publishers Ltd. New Delhi, Association with kluwer Academic Publishers, Boston, 1996.
- [25] A. Rajapakse, K. Furuta, and S. Kondo, “Evolutionary learning of fuzzy logic controllers and their adaptation through perpetual evolution,” IEEE Trans. on Fuzzy Systems, Vol.10, No.3, pp. 309-321, 2002.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.