Skip to main content
SpringerLink
Log in

Neuro-control to Energy Minimization for a Class of Chaotic Systems Based on ADP Algorithm

  • Conference paper
Book cover Intelligence Science and Big Data Engineering (IScIDE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8261))

  • 2305 Accesses

Abstract

This paper discusses the energy minimization problem of a class of chaotic systems, and constructs an optimal neuro-controller based on adaptive dynamic programming (ADP) algorithm. To learn the optimal performance index and control policy, an iterative algorithm is established. To prove the convergence of the presented iterative algorithm, theorems with rigorous and detailed proofs are given. It is proven that the iterative performance index functions are monotone decreasing and converge to the minimum energy. A simulation example is used to indicate that the presented energy minimization control method is effective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zhang, H., Huang, W., Wang, Z., Chai, T.: Adaptive synchronization between two different chaotic systems with unknown parameters. Physics Letters A 350(5-6), 363–366 (2006)

    Article  MATH  Google Scholar 

  2. Chen, S., Lü, J.: Synchronization of an uncertain unified chaotic system via adaptive control 14(4), 643–647 (2002)

    Google Scholar 

  3. Zhang, H., Wang, Z., Liu, D.: Chaotifying fuzzy hyperbolic model using adaptive inverse optimal control approach 14(10), 3505–3517 (2004)

    Google Scholar 

  4. Ma, T., Fu, J.: Global exponential synchronization between L system and Chen system with unknown parameters and channel time-delay. Chinese Physics B 20(5), 050511 (2011)

    Article  Google Scholar 

  5. Ma, T., Fu, J., Sun, Y.: An improved impulsive control approach to robust lag synchronization between two different chaotic systems. Chinese Physics B 19(9), 090502 (2010)

    Google Scholar 

  6. Ma, T., Zhang, H., Fu, J.: Exponential synchronization of stochastic impulsive perturbed chaotic Lur’e systems with time-varying delay and parametric uncertainty. Chinese Physics B 17(12), 4407–4417 (2008)

    Article  Google Scholar 

  7. Zhang, H., Ma, T., Fu, J., Tong, S.: Robust lag synchronization of two different chaotic systems via dual-stage impulsive control. Chinese Physics B 18(9), 3751–3757 (2009)

    Article  Google Scholar 

  8. Song, R., Xiao, W., Sun, C., Wei, Q.: Approximation-Error-ADP-Based Optimal Tracking Control for Chaotic Systems With Convergence Proof. Chinese Physics B (accept)

    Google Scholar 

  9. Murray, J., Cox, C., Lendaris, G., Saeks, R.: Adaptive dynamic programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 32(2), 140–153 (2002)

    Article  Google Scholar 

  10. Seiffertt, J., Sanyal, S., Wunsch, D.: Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38(4), 918–923 (2008)

    Article  Google Scholar 

  11. He, P., Jagannathan, S.: Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 37(2), 425–436 (2007)

    Article  Google Scholar 

  12. Zhao, Y., Patek, S., Beling, P.: Decentralized Bayesian search using approximate dynamic programming methods. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38(4), 970–975 (2008)

    Article  Google Scholar 

  13. Werbos, P.: Advanced forecasting methods for global crisis warning and models of intelligence. General Systems Yearbook 22, 25–38 (1977)

    Google Scholar 

  14. Zheng, C., Jagannathan, S.: Generalized Hamilton-Jacobi-Bellman formulation-based neural network control of affine nonlinear discrete-time systems. IEEE Transactions on Neural Networks 19(1), 90–106 (2008)

    Article  Google Scholar 

  15. Powell, W.: Approximate dynamic programming: solving the curses of dimensionality. Wiley, New York (2009)

    Google Scholar 

  16. He, P., Jagannathan, S.: Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 37(2), 425–436 (2007)

    Article  Google Scholar 

  17. Al-Tamimi, A., Lewis, F., Abu-Khalaf, M.: Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control. Automatica 43, 473–481 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Vrabie, D., Pastravanu, O., Abu-Khalaf, M., Lewis, F.: Adaptive optimal control for continuous-time linear systems based on policy iteration. Automatica 45(2), 477–484 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  19. Vamvoudakis, K., Lewis, F.: Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5), 878–888 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. Murray, J., Cox, C., Lendaris, G., Saeks, R.: Adaptive dynamic programming. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 32(2), 140–153 (2002)

    Article  Google Scholar 

  21. Wang, F., Jin, N., Liu, D., Wei, Q.: Adaptive dynamic programming for finite horizon optimal control of discrete-time nonlinear systems with ε-error bound. IEEE Transactions on Neural Networks 22(1), 24–36 (2011)

    Article  Google Scholar 

  22. Zhang, H., Wei, Q., Liu, D.: An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games. Automatica 47(1), 207–214 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Si, J., Wang, Y.: On-line learning control by association and reinforcement. IEEE Transactions on Neural Networks 12(2), 264–276 (2001)

    Article  MathSciNet  Google Scholar 

  24. Enns, R., Si, J.: Helicopter trimming and tracking control using direct neural dynamic programming. IEEE Transactions on Neural Networks 14(4), 929–939 (2003)

    Article  Google Scholar 

  25. Zhang, H., Wei, Q., Luo, Y.: A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38(4), 937–942 (2008)

    Article  Google Scholar 

  26. Zhang, H., Luo, Y., Liu, D.: Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints. IEEE Transactions on Neural Networks 20, 1490–1503 (2009)

    Article  Google Scholar 

  27. Wei, Q., Zhang, H., Dai, J.: Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing 72(7-9), 1839–1848 (2009)

    Article  Google Scholar 

  28. Wang, D., Liu, D., Wei, Q., Zhao, D.: Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming. Automatica 48(8), 1825–1832 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Ruizhuo Song & Wendong Xiao

  2. The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Qinglai Wei

Authors
  1. Ruizhuo Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wendong Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qinglai Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Automation and Electrical Engineering, University of Science and Technology, Xueyuan Road No. 30, 100083, Beijing, China

    Changyin Sun

  2. Department of Psychology, Peking University, Yiheyuan Road No. 5, 100871, Beijing, China

    Fang Fang

  3. Department of Computer Science and Technology, Nanjing University, Xianlin Avenue No. 163, 210023, Nanjing, China

    Zhi-Hua Zhou

  4. School of Automation, Southeast University, Sipailou No. 2, 210096, Nanjing, China

    Wankou Yang

  5. Institute of Automation, Chinese Academy of Sciences, No. 95 East Zhongguancun Road, 100190, Beijing, China

    Zhi-Yong Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Song, R., Xiao, W., Wei, Q. (2013). Neuro-control to Energy Minimization for a Class of Chaotic Systems Based on ADP Algorithm. In: Sun, C., Fang, F., Zhou, ZH., Yang, W., Liu, ZY. (eds) Intelligence Science and Big Data Engineering. IScIDE 2013. Lecture Notes in Computer Science, vol 8261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42057-3_78

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-42057-3_78

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-42056-6

  • Online ISBN: 978-3-642-42057-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation