Statistic Tracking Control: A Multi-objective Optimization Algorithm

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3972)

Abstract

This paper addresses a new type of control framework for dynamical stochastic systems, which is called statistic tracking control here. General non-Gaussian systems are considered and the tracked objective is the statistic information (including the moments and the entropy) of a given target probability density function (PDF), rather than a deterministic signal. The control is aiming at making the statistic information of the output PDFs to follow those of a target PDF. The B-spline neural network with modelling error is applied to approximate the corresponding dynamic functional. For the nonlinear weighting system with time delays in the presence of exogenous disturbances, the generalized H2 and H ∞  optimization technique is then used to guarantee the tracking, robustness and transient performance simultaneously in terms of LMI formulations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with Applications to Tracking and Navigation. John Wiley & Sons, London (2001)CrossRefGoogle Scholar
  2. 2.
    Crespo, L.G., Sun, J.Q.: Nonlinear Stochastic Control via Stationary Probability Density Functions. In: Proc. ACC, Anchorage, AK, USA, pp. 2029–2033 (2002)Google Scholar
  3. 3.
    Forbes, M.G., Forbes, J.F., Guay, M.: Regulatory Control Design for Stochastic Processes: Shaping the Probability Density Function. In: Proc. ACC 2003, Denver, USA, pp. 3998–4003 (2003)Google Scholar
  4. 4.
    Goodwin, G.C., Sin, K.S.: Adaptive Filtering, Prediction and Control. Prentice- Hall, Englewood Cliffs (1984)MATHGoogle Scholar
  5. 5.
    Guo, L., Wang, H.: Fault Detection and Diagnosis for General Stochastic Systems Using B-Spline Expansions and Nonlinear Filters. IEEE Trans. on Circuits and Systems-I: Regular Papers 52, 1644–1652 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Guo, L., Wang, H.: Generalized Discrete-time PI Control of Output PDFs Using Square Root B-Spline Expansion. Automatica 41, 159–162 (2005)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Guo, L., Wang, H.: PID Controller Design for Output PDFs of Stochastic Systems Using Linear Matrix Inequalities. IEEE Trans. on Systems, Man and Cybernetics- Part B 35, 65–71 (2005)CrossRefGoogle Scholar
  8. 8.
    Guo, L., Zhang, Y.M., Feng, C.B.: Generalized H ∞  Performance and Mixed H2/H ∞  Optimization for Time Delay Systems. In: Proceedings of 8th Int. Conf. on Control, Automation, Robotics and Vision, Kunming, pp. 160–165 (2004)Google Scholar
  9. 9.
    Guo, L., Wang, H.: Minimum Entropy Filtering for Multivariate Stochastic Systems with Non-Gaussian Noises. IEEE Trans. on Automatic Control 51 (March 2006) (to appear)Google Scholar
  10. 10.
    Papoulis, A.: Probability, Random Variables and Stochastic Processes, 3rd edn. McGraw-Hill, New York (1991)Google Scholar
  11. 11.
    Wang, H.: Bounded Dynamic Stochastic Systems: Modelling and Control. Springer, London (2000)MATHGoogle Scholar
  12. 12.
    Yue, H., Wang, H.: Minimum Entropy Control of Closed Loop Tracking Errors for Dynamic Stochastic Systems. IEEE Trans. on Automatic Control 48, 118–122 (2003)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lei Guo
    • 1
  1. 1.Research Institute of AutomationSoutheast UniversityNanjingChina

Personalised recommendations