Advertisement

Stochastic Optimal Control of Nonlinear Jump Systems Using Neural Networks

  • Fei Liu
  • Xiao-Li Luan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3972)

Abstract

For a class of nonlinear stochastic Markovian jump systems, a novel feedback control law design is presented, which includes three steps. Firstly, the multi-layer neural networks are used to approximate the nonlinearities in the different jump modes. Secondly, the overall system is represented by the mode-dependent linear difference inclusion, which is suitable for control synthesis based on Lyapunov stability. Finally, by introducing stochastic quadratic performance cost, the existence of feedback control law is transformed into the solvability of a set of linear matrix inequalities. And the optimal upper bound of stochastic cost can be efficiently searched by means of convex optimization with global convergence assured.

Keywords

Linear Matrix Inequality Stochastic Optimal Control Markovian Jump System Linear Markovian Jump System Stochastic Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Krasovskii, N.N., Lidskii, E.A.: Analytical Design of Controllers in Systems with Random Attributes. Automat. Remote Control 22, 1021–1025 (1961)MathSciNetGoogle Scholar
  2. 2.
    Ji, Y., Chizeck, H.J.: Controllability, Stability and Continuous-time Markovian Jump Linear Quadratic Control. IEEE Trans. Automat. Contr. 35(7), 777–788 (1990)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fang, Y., Loparo, K.A.: Stabilization of Continuous-Time Jump Linear Systems. IEEE Trans. Automat. Contr. 47, 1590–1603 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Aliyu, M.D.S., Boukas, E.K.: Control for Markovian Jump Nonlinear Systems. In: Proc. IEEE Conf. Deci. Contr., pp. 766–771 (1998)Google Scholar
  5. 5.
    Wang, Z.D., Qiao, H., Burnham, K.J.: On Stabilization of Bilinear Uncertain Time-Delay Stochastic Systems with Markovian Jumping Parameters. IEEE Trans. Automat. Contr. 47(4), 640–646 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Nakura, G., Ichikawa, A.: Stabilization of A Nonlinear Jump System. Systems and Control Letters 47(4), 79–85 (2002)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bass, E., Lee, K.Y.: Robust Control of Nonlinear System Using Norm-Bounded Neural Networks. In: IEEE Int. Conf. Neural Networks, pp. 2524–2529 (1994)Google Scholar
  8. 8.
    Tanaka, K.: An Approach to Stability Criteria of Neural-Network Control Systems. IEEE Trans. Neural Networks 7(3), 629–642 (1996)CrossRefGoogle Scholar
  9. 9.
    Limanond, S., Si, J.: Neural-Network-Based Control Design: An LMI Approach. IEEE Trans. Neural Networks 9(6), 1422–1429 (1998)CrossRefGoogle Scholar
  10. 10.
    Wonham, W.M.: On A Matrix Riccati Equation of Stochastic Control. SIAM J. Contr. 6, 681–697 (1968)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fei Liu
    • 1
  • Xiao-Li Luan
    • 1
  1. 1.Institute of AutomationSouthern Yangtze UniversityWuxiP.R. China

Personalised recommendations