Advertisement

CMA—H Hybrid Design of Robust Stable Adaptive Fuzzy Controllers for Non-linear Systems

  • Kaushik Das Sharma
  • Amitava Chatterjee
  • Patrick Siarry
  • Anjan Rakshit
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)

Abstract

The present paper utilizes covariance matrix adaptation (CMA), an evolution strategy, in conjunction with H-based robust control law to design a stable adaptive fuzzy controller for a class of non-linear systems. The objective of the design is to develop a self-adaptive optimal/near optimal fuzzy controller, with guaranteed stability and satisfactory robust transient performance. The global search capability of CMA and H-based tuning, that provide a fast adaptation utilizing local search method, is employed in tandem with this proposed design methodology. The hybrid control strategy is implemented for benchmark simulation case study, and the results demonstrate the usefulness of the proposed approach.

Keywords

Covariance matrix adaptation (CMA) H based robust control Adaptive fuzzy control Hybrid fuzzy control Non-linear systems 

References

  1. 1.
    Hansen N., Ostermeier A., Gawelczyk A.: On the Adaptation of arbitrary normal mutation distributions in evolution strategies: the generating set adaptation. In: Proceedings of the 6th International Conference on Genetic Algorithms, San Francisco, CA, pp. 57–64 (1995)Google Scholar
  2. 2.
    Auger, A., Hansen, N.: A restart CMA evolution strategy with increasing population size. Congr. Evol. Comput. 2, 1769–1776 (2005)Google Scholar
  3. 3.
    Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.-P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical Report. Nanyang Tech. University. Singapore (2005)Google Scholar
  4. 4.
    Chen, B.S., Lee, C.H., Chang, Y.C.: H tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach. IEEE Trans. Fuzz. Syst. 4, 32–43 (1996)CrossRefGoogle Scholar
  5. 5.
    Das, Sharma K., Chatterjee, A., Rakshit, A.: a hybrid approach for design of stable adaptive fuzzy controllers employing Lyapunov theory and particle swarm optimization. IEEE Trans. Fuzzy Syst. 17, 329–342 (2009)CrossRefGoogle Scholar
  6. 6.
    Das, Sharma K., Chatterjee, A., Rakshit, A.: Design of a hybrid stable adaptive fuzzy controller employing Lyapunov theory and harmony search algorithm. IEEE Trans. Control Syst. Technol. 18, 1440–1447 (2010)Google Scholar
  7. 7.
    Fischle, K., Schroder, D.: An improved stable adaptive fuzzy control method. IEEE Trans. Fuzzy Syst. 7, 27–40 (1999)CrossRefGoogle Scholar
  8. 8.
    Tong, S., Li, H.X., Wang, W.: Observer-based adaptive fuzzy control for SISO nonlinear systems. Fuzz. Sets Syst. 148, 355–376 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9, 159–195 (2001)CrossRefGoogle Scholar
  10. 10.
    Hansen, N., Muller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11, 1–18 (2003)CrossRefGoogle Scholar
  11. 11.
    Hansen, N., Kern, S.: Evaluating the CMA evolution strategy on multimodal test functions. In: Parallel Problem Solving from Nature—PPSN VIII. Lecture Notes in Computer Science, vol. 3242, pp. 282–291 (2004)Google Scholar
  12. 12.
    Das Sharma, K., Chatterjee, A., Matsuno, F.: A Lyapunov theory and stochastic optimization based stable adaptive fuzzy control methodology. In: Proceedings of the SICE Annual Conference 2008, Japan, pp. 1839–1844 (2008)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Kaushik Das Sharma
    • 1
  • Amitava Chatterjee
    • 2
  • Patrick Siarry
    • 3
  • Anjan Rakshit
    • 2
  1. 1.Department of Applied PhysicsUniversity of CalcuttaKolkataIndia
  2. 2.Department of Electrical EngineeringJadavpur UniversityKolkataIndia
  3. 3.Lab. LiSSiUniversité Paris-Est CréteilVitry-sur-SeineFrance

Personalised recommendations