Journal of Zhejiang University SCIENCE C

, Volume 15, Issue 1, pp 43–50

Adaptive dynamic programming for linear impulse systems

Authors

  • Xiao-hua Wang
    • School of Mechatronics Engineering and AutomationShanghai University
    • Shanghai Key Laboratory of Power Station Automation TechnologyShanghai University
  • Juan-juan Yu
    • School of Mechatronics Engineering and AutomationShanghai University
  • Yao Huang
    • School of Mechatronics Engineering and AutomationShanghai University
  • Hua Wang
    • School of Mechatronics Engineering and AutomationShanghai University
    • Shanghai Key Laboratory of Power Station Automation TechnologyShanghai University
    • School of Mechatronics Engineering and AutomationShanghai University
    • Shanghai Key Laboratory of Power Station Automation TechnologyShanghai University
Article

DOI: 10.1631/jzus.C1300145

Cite this article as:
Wang, X., Yu, J., Huang, Y. et al. J. Zhejiang Univ. - Sci. C (2014) 15: 43. doi:10.1631/jzus.C1300145

Abstract

We investigate the optimization of linear impulse systems with the reinforcement learning based adaptive dynamic programming (ADP) method. For linear impulse systems, the optimal objective function is shown to be a quadric form of the pre-impulse states. The ADP method provides solutions that iteratively converge to the optimal objective function. If an initial guess of the pre-impulse objective function is selected as a quadratic form of the pre-impulse states, the objective function iteratively converges to the optimal one through ADP. Though direct use of the quadratic objective function of the states within the ADP method is theoretically possible, the numerical singularity problem may occur due to the matrix inversion therein when the system dimensionality increases. A neural network based ADP method can circumvent this problem. A neural network with polynomial activation functions is selected to approximate the pre-impulse objective function and trained iteratively using the ADP method to achieve optimal control. After a successful training, optimal impulse control can be derived. Simulations are presented for illustrative purposes.

Key words

Adaptive dynamic programming (ADP)Impulse systemOptimal controlNeural network

CLC number

TP273.1

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2014