Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

A Study on a Stochastic Nonlinear System Control Using Neural Networks

신경회로망을 사용한 비선형 확률시스템 제어에 관한 연구

  • 석진욱 (홍익대학교 과학기술연구소) ;
  • 최경삼 (홍익대하교 전자전기공학부) ;
  • 조성원 (홍익대하교 전자전기공학부) ;
  • 이종수 (홍익대하교 전자전기공학부)
  • Published : 2000.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we give some geometric condition for a stochastic nonlinear system and we propose a control method for a stochastic nonlinear system using neural networks. Since a competitive learning neural networks has been developed based on the stochastcic approximation method it is regarded as a stochastic recursive filter algorithm. In addition we provide a filtering and control condition for a stochastic nonlinear system called the perfect filtering condition in a viewpoint of stochastic geometry. The stochastic nonlinear system satisfying the perfect filtering condition is decoupled with a deterministic part and purely semi martingale part. Hence the above system can be controlled by conventional control laws and various intelligent control laws. Computer simulation shows that the stochastic nonlinear system satisfying the perfect filtering condition is controllable and the proposed neural controller is more efficient than the conventional LQG controller and the canonical LQ-Neural controller.

Keywords

References

  1. A. Isidori, 'Nonlinear control systems', 3rd ED. Springer-Verlarg : London, 1995
  2. A. Isidori, 'Disturbance attenuation and $H_{\infty}$ control via measurement feedback in nonlinear systems', IEEE Trans. on Automatic Control, vol. 37, pp. 1283-1293, 1992 https://doi.org/10.1109/9.159566
  3. G. Blankenship, C-H Liu, and S. Marcus, 'Asymtotic expansions and lie algebras for some nonlinear filtering problems', IEEE Trans. on Automatic Control, vol. AC-28, no. 7, July 1983
  4. 주성준, 서진헌, '부분 선형화 가능한 미지구조를 자기는 비선형 시스템', 전기학회 논문지, 57권, 3호, pp 349-357, 1998년 3월
  5. G. Chen, G. Chem, S-H and Hsu, 'Linear stochastic control systems', CRC Press : Boca Raton, 1995
  6. H J Kushner and P. G. Dupuis, 'Numerical methods for stochastic control problems in continuous time', Springer-Verlag : New York, 1992
  7. P. S. Maybeck, 'Stochastic models, estimation, and control volume 3'. Academic Press : New York, 1982
  8. N. Ikeda and S. Watanabe, 'Stochastic diffrential equations and diffusion process'. 2nd Ed. North-Holland, 1989
  9. K. Sobczyk, 'Stochastic diffrential equations with applications to physics and engineering', Kluwer Academy, Dordrecht, 1991
  10. M. Freidlin, 'Markov processes and differential equations : asymtotic problems', Birkhauser : Zurich, 1997
  11. 석진욱, 조성원, 'Fokker-Plank 방정식의 해석을 통한 Langevine 경쟁학습의 동역학 분석', 대한전자공학회 논문지, 제34권, C편, 제7호, pp. 82-91, 1997
  12. Jinwuk Seok and Seongwon Cho, 'Quotient canonical feature map competitive learning', Proc. IEEE Asia Pacific Conf. on Circuits and Systems 96, pp. 528-531, 1996 https://doi.org/10.1109/APCAS.1996.569330
  13. G. Chen, G. Chen and S-H. Hsu, 'Linear stochastic control systems', CRC Press : Boca Raton, 1995