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Selection and impact of different topologies in multi-layered hierarchical fuzzy systems

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Abstract

An evolutionary algorithm based approach for selection of topologies in hierarchical fuzzy systems (HFS) is presented. Coupling fuzzy system with evolutionary algorithm provides a solution to the automated acquisition of the fuzzy rule base. It is difficult to study the problem of hierarchical decomposition for a large class of fuzzy systems but it is possible to analyse such architectures on the example of a particular fuzzy system, such as inverted pendulum. Topology of the HFS must be selected according to the physical properties of the dynamical system under consideration. Different HFS topologies for an inverted pendulum system are investigated and analysed to address the problem of how input configuration in multi-layered structure affects the controller performance. The experiments are conducted to test controller performance for different topologies of the hierarchical fuzzy system. The impact of different topologies on control process is discussed. The results from the case study of inverted pendulum can be extended to other dynamical systems.

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References

  1. Cordon O, Herrera F, Hoffmann F, Magdalena L (2001) Genetic fuzzy systems: evolutionary tuning and learning of fuzzy knowledge bases. Advances in fuzzy systems applications and theory, vol 19. World Scientific, Singapore

    MATH  Google Scholar 

  2. Cordon O, Herrera F, Zwir I (2001) Linguistic modeling of hierarchical systems of linguistic rules. IEEE Trans Fuzzy Syst 10(1):2–20

    Article  Google Scholar 

  3. Konar A (2005) Computational intelligence. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Babuska R (2009) Computational intelligence in modelling and control. Delft University of Technology. http://www.dcsc.tudelft.nl/~rbabuska/CTU/transp/lecture_notes_ctu.pdf

  5. Zadeh LA (1973) Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans Syst Man Cybern 3(1):177–200

    Article  MathSciNet  Google Scholar 

  6. Pedrycz W (1984) An identification algorithm in fuzzy relational systems. Fuzzy Sets Syst 13:153–167

    Article  MathSciNet  MATH  Google Scholar 

  7. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modelling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    MATH  Google Scholar 

  8. Raju GVS, Zhou J, Kisner RA (1991) Hierarchical fuzzy control. Int J Control, 54(5):1201–1216

    Article  MathSciNet  MATH  Google Scholar 

  9. Zajaczkowski J, Verma B (2010) An evolutionary algorithm based approach for selection of topologies in hierarchical fuzzy systems. In: WCCI 2010 IEEE World congress on computational intelligence, CCIB, Barcelona, Spain, July 18–23, 2010, pp 976–983

    Google Scholar 

  10. Zajaczkowski J, Stonier RJ (2008) Analysis of hierarchical control for the inverted pendulum. Complex Int 12:msid49. http://www.complexity.org.au/vol12/msid49/

    Google Scholar 

  11. Stonier RJ, Stacey AJ, Messom C (1998) Learning fuzzy controls for the inverted pendulum. In: Proceedings of ISCA 7th international conference on intelligent systems, Melun, pp 64–67

    Google Scholar 

  12. Chen CS, Chen WL (1998) Robust adaptive sliding-mode control using fuzzy modelling for an inverted-pendulum system. IEEE Trans Ind Electron 45(2):297–306

    Article  Google Scholar 

  13. Chen BS, Uang HJ, Tseng CS (1999) Robustness design of nonlinear dynamic systems via fuzzy linear control. IEEE Trans Fuzzy Syst 7(5):571–585

    Article  Google Scholar 

  14. Zhong W, Rock H (2001) Energy and passivity based control of the double inverted pendulum on a cart. In: 2001 IEEE conference on control applications, pp 896–901

    Google Scholar 

  15. Durr P, Mattiussi C (2010) Genetic representation and evolvability of modular neural controllers. IEEE Comput Intell Mag, 11–19. doi:10.1109/MCI.2010.937319

  16. Acampora G (2010) Exploiting timed automata-based fuzzy controllers and data mining to detect computer network intrusions. In: WCCI 2010 IEEE World congress on computational intelligence, FUZZ, Barcelona, Spain, July 18–23, 2010, pp 1381–1388

    Google Scholar 

  17. Acampora G, Loia V, Vitiello A (2010) Hybridizing fuzzy control and timed automata for modeling variable structure fuzzy systems. In: WCCI 2010 IEEE World congress on computational intelligence, FUZZ, Barcelona, Spain, July 18–23, 2010, pp 1894–1901

    Google Scholar 

  18. Hsu YC, Chen G, Li HX (2001) A fuzzy adaptive variable structure controller with applications to robot manipulators. IEEE Trans Syst Man Cybern, Part B, Cybern 31(3):331–340

    Article  Google Scholar 

  19. Huang YP, Wang SF (2000) Designing a fuzzy model by adaptive macroevolution genetic algorithms. Fuzzy Sets Syst 113:367–379

    Article  MATH  Google Scholar 

  20. Abraham A (2005) Adaptation of fuzzy inference system using neural learning, fuzzy system engineering: theory and practice. In: Nedjah N et al (eds) Studies in fuzziness and soft computing, Chap. 3. Springer, Berlin, pp 53–83

    Google Scholar 

  21. Chen Y, Yang B, Abraham A, Peng L (2007) Automatic design of hierarchical Takagi-Sugeno type fuzzy systems using evolutionary algorithms. IEEE Trans Fuzzy Syst 15(3):385–397. doi:10.1016/S0020-0255(01)00140-2

    Article  MATH  Google Scholar 

  22. Torra V (2002) A review of the construction of hierarchical fuzzy systems. Int J Intell Syst 17(5):531–543. doi:10.1002/int.10036

    Article  MathSciNet  MATH  Google Scholar 

  23. Tunstel E, de Oliveira MAA, Berman S (2002) Fuzzy behavior hierarchies for multi-robot control. Int J Intell Syst 17(5):449–470. doi:10.1002/int.10032

    Article  MATH  Google Scholar 

  24. Magdalena L (2002) On the role of context in hierarchical fuzzy controllers. Int J Intell Syst 17(5):471–493. doi:10.1002/int.10033

    Article  MATH  Google Scholar 

  25. Tachibana K, Furuhashi T (2002) A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm. Int J Intell Syst 17(5):495–513. doi:10.1002/int.10034

    Article  MATH  Google Scholar 

  26. Kikuchi H, Takagi N (2002) Hierarchical fuzzy modeling and jointly expandable functions. Int J Intell Syst 17(5):515–529. doi:10.1002/int.10035

    Article  MATH  Google Scholar 

  27. Lee ML, Chung HY, Yu FM (2003) Modeling of hierarchical fuzzy systems. Fuzzy Sets Syst 138(2):343–361. doi:10.1016/S0165-0114(02)00517-1

    Article  MathSciNet  Google Scholar 

  28. Cordon O, Herrera F, Zwir I (2002) A hierarchical knowledge-based environment for linguistic modeling: models and iterative methodology. Fuzzy Sets Syst 138(2):307–341. doi:10.1016/j.asoc.2006.12.001

    Article  MathSciNet  Google Scholar 

  29. Delgado MR, von Zuben F, Gomide F (2003) Hierarchical genetic fuzzy systems. Fuzzy Sets Syst 138(2):307–341. doi:10.1016/S0165-0114(02)00388-3

    Article  Google Scholar 

  30. Sushmita S, Chaudhury S (2007) Hierarchical fuzzy case based reasoning with multi-criteria decision making for financial applications. In: Pattern recognition and machine intelligence. Lecture notes in computer science, vol 4815/2007. Springer, Berlin, pp 226–234 doi:10.1007/978-3-540-77046-6_28

    Chapter  Google Scholar 

  31. Cheong F (2008) A hierarchical fuzzy system with high input dimensions for forecasting foreign exchange rates. International J Artif Intell Soft Comput 1(1):15–24

    Article  Google Scholar 

  32. Stonier RJ, Mohammadian M (2004) Multi-layered and hierarchical fuzzy modelling using evolutionary algorithms. In: Proceedings of CIMCA’2004, Gold Coast, pp 321–344

    Google Scholar 

  33. Yager RR (1998) On the construction of hierarchical fuzzy systems models. IEEE Trans Syst Man Cybern 28(1):55–66

    Article  Google Scholar 

  34. Holve R (1997) Rule generation for hierarchical fuzzy systems. In: Fuzzy information processing society, 1997, NAFIPS ’97, pp 444–449. doi:10.1109/NAFIPS.1997.624082

    Google Scholar 

  35. Sindelar R (2005) Hierarchical fuzzy systems. In: Proceedings of the 16th IFAC World congress, 2005, vol 15(1). doi:10.3182/20050703-6-CZ-1902.01119

    Google Scholar 

  36. Mon YJ, Lin CM (2002) Hierarchical fuzzy sliding-mode control. In: Proceedings of the 2002 IEEE World congress on computational intelligence, pp 656–661. doi:10.1109/FUZZ.2002.1005070

    Google Scholar 

  37. Yeh ZM, Li KH (2004) A systematic approach for designing multistage fuzzy control systems. Fuzzy Sets Syst 143(2):251–273

    Article  MathSciNet  MATH  Google Scholar 

  38. Dasgupta D (1998) Evolving neuro-controllers for a dynamic system using structured genetic algorithm. Appl Intell 8:113–121

    Article  Google Scholar 

  39. Wang W, Yi J, Zhao DX, Liu X (2005) Design of cascade fuzzy sliding-mode controller. In: 2005 American control conference, Portland, USA, pp 4649–4654

    Chapter  Google Scholar 

  40. Cheong F, Lai R (2007) Designing a hierarchical fuzzy controller using the differential evolution approach. Appl Soft Comput 7(2):481–491

    Article  Google Scholar 

  41. Magdalena L (1998) Hierarchical fuzzy control of a complex system using meta-knowledge. In: Proceedings of the 7th international conference on information processing and management of uncertainty in knowledge-based systems, pp 630–637

    Google Scholar 

  42. Lei S, Langari R (2003) Synthesis and approximation of fuzzy logic controllers for nonlinear systems. Int J Fuzzy Syst 5(2):98–105

    MathSciNet  Google Scholar 

  43. Lin CM, Mon YJ (2005) Decoupling control by hierarchical fuzzy sliding-mode controller. IEEE Trans Control Syst Technol 13(4):593–589

    Article  Google Scholar 

  44. Shuliang L, Langari R (2000) Hierarchical fuzzy logic control of a double inverted pendulum. In: Fuzzy system 2000, FUZZ IEEE 2000, 9th IEEE international conference, vol 2, pp 1074–1077

    Google Scholar 

  45. Castillo O, Cazarez N, Rico D (2006) Intelligent control of dynamic systems using type-2 fuzzy logic and stability issues. Int Math Forum 1(28):1371–1382

    MathSciNet  MATH  Google Scholar 

  46. Raju S, Zhou J (1993) Adaptive hierarchical fuzzy controller. IEEE Trans Syst Man Cybern 23(4):973–980

    Article  Google Scholar 

  47. Yi J, Yubazaki N (2000) Stabilization fuzzy control of inverted pendulum systems. Artif Intell Eng 14:153–163

    Article  Google Scholar 

  48. Yu WS, Sun CJ (2001) Fuzzy model based adaptive control for a class of nonlinear systems. IEEE Trans Fuzzy Syst 9:413–425

    Article  Google Scholar 

  49. Chang W, Park JB, Joo YH, Chen G (2002) Design of robust fuzzy-model based controller with sliding mode control for SISO nonlinear systems. Fuzzy Sets Syst 125:1–22

    Article  MathSciNet  MATH  Google Scholar 

  50. Koo TJ (2001) Stable model reference adaptive fuzzy control of a class of nonlinear systems. IEEE Trans Fuzzy Syst 9(4):624–636

    Article  MathSciNet  Google Scholar 

  51. Qiao F, Zhu QM, Winfield A, Melhuish C (2003) Fuzzy sliding mode control for discrete nonlinear systems. Trans China Autom Soc 22(2):313–315

    Google Scholar 

  52. Wang LX (1997) A course in fuzzy systems and control. Prentice Hall, New York

    MATH  Google Scholar 

  53. Khan SA, Engelbrecht AP (2010) A fuzzy particle swarm optimization algorithm for computer communication network topology design. Appl Intell. doi:10.1007/s10489-010-0251-2

    Google Scholar 

  54. Gacto MJ, Alcala R, Herrera F (2010) A multi-objective evolutionary algorithm for an effective tuning of a fuzzy logic controllers in heating, ventilating and air conditioning systems. Appl Intell. doi:10.1007/s10489-010-0264-x

    Google Scholar 

  55. Erus G, Polat F (2007) A layered approach to learning coordination knowledge in multiagent environments. Appl Intell 27:249–267. doi:10.1007/s10489-006-0034-y

    Article  Google Scholar 

  56. Chen CM (2005) A hierarchical neural network document classifier with linguistic feature selection. Appl Intell 23:277–294

    Article  Google Scholar 

  57. Hong TP, KY Lin, Chien BC (2003) Mining fuzzy multiple-level association rules from quantitative data. Appl Intell 18:79–90

    Article  MATH  Google Scholar 

  58. Cho SB, Shimohara K (1998) Evolutionary learning of modular neural networks with genetic programming. Appl Intell 9:191–200

    Article  Google Scholar 

  59. Akole M, Tyagi B (2008) Design of fuzzy logic controller for nonlinear model of inverted pendulum-cart system. In: XXXII national systems conference NSC 2008, pp 750–755

    Google Scholar 

  60. Beceriklia Y, Celik BK (2007) Fuzzy control of inverted pendulum and concept of stability using Java application. Math Comput Model 46(1–2):24–37

    Article  Google Scholar 

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Correspondence to Juliusz Zajaczkowski.

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Zajaczkowski, J., Verma, B. Selection and impact of different topologies in multi-layered hierarchical fuzzy systems. Appl Intell 36, 564–584 (2012). https://doi.org/10.1007/s10489-011-0277-0

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