Abstract
Based on the genetic algorithm (GA), an approach is proposed for simultaneous design of membership functions and fuzzy control rules since these two components are interdependent in designing a fuzzy logic controller (FLC). With triangular membership functions, the left and right widths of these functions, the locations of their peaks, and the fuzzy control rules corresponding to every possible combination of input linguistic variables are chosen as parameters to be optimized. By using a proportional scaling method, these parameters are then transformed into real-coded chromosomes, over which the offspring are generated by rank-based reproduction, convex crossover, and nonuniform mutation. Meanwhile, the concept of enlarged sampling space is used to expedite the convergence of the evolutionary process. To show the feasibility and validity of the proposed method, a cart-centering example will be given. The simulation results will show that the designed FLC can drive the cart system from any given initial state to the desired final state even when the cart mass varies within a wide range.
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References
Chang, C. H. and Wu, Y. C.: The genetic algorithm-based tuning method for symmetric membership functions of fuzzy logic control systems, in: Proc. of the Internat. IEEE/IAS Conf. on Industrial Automation and Control: Emerging Technologies, 1995, pp. 421-428.
Fogel, D.: An introduction to simulated evolutionary optimization, IEEE Trans. Neural Networks 5 (1994), 3-14.
Gen, M. and Cheng, R.: Genetic Algorithm and Engineering Design, Wiley, New York, 1997.
Goldberg, D. E.: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
Grefenstette, J. J.: Optimization of control parameters for genetic algorithms, IEEE Trans. Systems Man Cybernet. 16(1) (1986), 122-128.
Holland, J.: Adaptation in Natural and Artificial System, Univ. of Michigan Press, Ann Arbor, 1975.
Homaifar, A. and McCormick, E.: Simultaneous design of membership functions and rule sets for fuzzy controller using genetic algorithms, IEEE Trans. Fuzzy Systems 3(2) (1995), 129-139.
Karr, C. L. and Gentry, E. J.: Fuzzy control of pH using genetic algorithms, IEEE Trans. Fuzzy Systems 1(1) (1993), 46-53.
Lee, C. C.: Fuzzy logic in control systems: Fuzzy logic controller-Part I, IEEE Trans. Systems Man Cybernet. 20 (1990), 404-418.
Mamdani, E. H.: Applications of fuzzy algorithms for control of simple dynamic plant, Proc. IEE 121(12) (1974), 1585-1588.
Man, K. F., Tang, K. S., and Kwong, S.: Genetic algorithms: Concepts and applications, IEEE Trans. Industr. Electronics 43(5) (1996), 519-534.
Michalewicz, Z.: Genetic Algorithm C Data Structure D Evolution Programs, 2nd ed., Springer, New York, 1994.
Schwefel, H.: Evolution and Optimum Seeking, Wiley, New York, 1994.
Tang, K. S., Chan, C. Y., and Man, K. F.: A simultaneous method for fuzzy memberships and rules optimization, in: Proc. of the IEEE Internat. Conf. on Industrial Technology, 1996, pp. 279-283.
Thrift, P.: Fuzzy logic synthesis with genetic algorithms, in: Proc. of the 4th Internat. Conf. on Genetic Algorithms, 1991, pp. 450-457.
Zadeh, L. A.: Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man Cybernet. 3 (1973), 28-44.
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Wu, CJ., Liu, GY. A Genetic Approach for Simultaneous Design of Membership Functions and Fuzzy Control Rules. Journal of Intelligent and Robotic Systems 28, 195–211 (2000). https://doi.org/10.1023/A:1008186427312
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DOI: https://doi.org/10.1023/A:1008186427312