A Reliable Control of Nonlinear Systems via a Sum of Squares Approach

제곱합 접근법에 의한 비선형시스템의 신뢰성제어

  • 류석환 (대구대학교 전자전기공학부)
  • Received : 2012.03.22
  • Accepted : 2012.06.01
  • Published : 2012.06.25

Abstract

This paper deals with a design of reliable state feedback controllers for continuous time polynomial systems with actuator failures. The goal is to find an asymptotically stabilizing controller such that the closed loop system achieves the prescribed decay rate in the actuator failure cases. Based on a sum of squares (SOS) approach, a design method for reliable nonlinear controller is presented. In order to demonstrate our design method, a numerical example is shown.

Keywords

Acknowledgement

Supported by : 대구대학교

References

  1. R. J. Veillette, J. V. Medanic and W. R. Perkins(1992), "Design of Reliable Control Systems", IEEE Trans. on Automatic Control, Vol.37, No.3, pp. 290-304 https://doi.org/10.1109/9.119629
  2. B. Yao and X. He(2006), "Guaranteed Cost Reliable Control for Discrete-Time Linear Systems", Proceedings of the 6th World Congress on Intelligent Control and Automation, pp. 1294-1298, June 21-23, Dalian, China
  3. G. H. Yang, J. Lam and J. Wang(1998), "Reliable $H_{\infty}$ Control for Affine Nonlinear Systems", IEEE Trans. on Automatic Control, Vol.43, No.8, pp. 1112-1117 https://doi.org/10.1109/9.704984
  4. L. Zhang, S. Wu, L. Zhang and J. Zhang(2006), "Adaptive Reliable and Robust $H_{\infty}$ Control for Nonlinear Systems with Parametric Uncertainties and External Disturbances", Control, Automation, Robotics and Vision ICARCV'06 9th International Conference, Dec. 5-8, pp. 1-4
  5. H. Wu and H. Zhang(2006), "Reliable $H_{\infty}$ Fuzzy Control for Continuous Time Nonlinear Systems with Actuator Failures", IEEE Trans. on Fuzzy Systems, Vol.14, No.5, pp. 609-618 https://doi.org/10.1109/TFUZZ.2006.876723
  6. A. Papachristodoulou and S. Prajna(2005), "Analysis of Non-polynomial Systems using the Sum of Squares Decomposition", pp. 1-20, Positive Polynomials in Control, Springer
  7. K. Tanaka, K. Yamauchi, H. Ohtake and H. O. Wang(2007), "Guaranteed Cost Control of Polynomial Fuzzy Systems via a Sum of Squares Approach", Proceedings of the 46th IEEE Conference on Decision and Control, pp.5954-5959, New Orleans, LA, Dec. 12-14
  8. K. Tanaka, H. Ohtake, M. Wada, H. O. Wang and Y. Chen(2009), "Polynomial Fuzzy Observer Design: A Sum of Squares Approach", Proceedings of the 48th IEEE Conference on Decision and Control, pp.7771-7776, Shanghai, P.R.China, Dec. 16-18
  9. S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan(1994), "Linear Matrix Inequalities in System and Control Theory", SIAM studies in applied mathmatics, Vol.15