Skip to main content

Event-Triggered H  ∞  Control for Continuous-Time Nonlinear System

  • Conference paper
  • First Online:
Book cover Advances in Neural Networks – ISNN 2015 (ISNN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

Included in the following conference series:

Abstract

In this paper, the H  ∞  optimal control for a class of continuous-time nonlinear systems is investigated using event-triggered method. First, the H  ∞  optimal control problem is formulated as a two-player zero-sum differential game. Then, an adaptive triggering condition is derived for the closed loop system with an event-triggered control policy and a time-triggered disturbance policy. For implementation purpose, the event-triggered concurrent learning algorithm is proposed, where only one critic neural network is required. Finally, an illustrated example is provided to demonstrate the effectiveness of the proposed scheme.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basar, T., Olsder, G.J., Clsder, G.J., et al.: Dynamic noncooperative game theory. Academic Press, London (1995)

    MATH  Google Scholar 

  2. Zhao, D., Zhu, Y.: MEC—A Near-Optimal Online Reinforcement Learning Algorithm for Continuous Deterministic Systems. IEEE Transactions on Neural Networks and Learning Systems 26(2), 346–356 (2015)

    Article  MathSciNet  Google Scholar 

  3. Zhao, D., Xia, Z., Wang, D.: Model-Free Optimal Control for Affine Nonlinear Systems With Convergence Analysis. IEEE Transactions on Automation Science and Engineering (2015), doi:10.1109/TASE.2014.2348991

    Google Scholar 

  4. Alippi, C., Ferrero, A., Piuri, V.: Artificial intelligence for instruments and measurement applications. IEEE Instrumentation & Measurement Magazine 1(2), 9–17 (1998)

    Article  Google Scholar 

  5. Al-Tamimi, A., Abu-Khalaf, M., Lewis, F.L.: Adaptive critic designs for discrete-time zero-sum games with application to control. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 37(1), 240–247 (2007)

    Article  MATH  Google Scholar 

  6. Abu-Khalaf, M., Lewis, F.L., Huang, J.: Policy iterations on the Hamilton-Jacobi-Isaacs equation for state feedback control with input saturation. IEEE Transactions on Automatic Control 51(12), 1989–1995 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Vamvoudakis, K.G., Lewis, F.L.: Online solution of nonlinear two-player zero-sum games using synchronous policy iteration. International Journal of Robust and Nonlinear Control 22(13), 1460–1483 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Sahoo, A., Xu, H., Jagannathan, S.: Event-based optimal regulator design for nonlinear networked control systems. In: 2014 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, pp. 1–8. IEEE Press, Orlando (2014)

    Google Scholar 

  9. Zhong, X., Ni, Z., He, H., Xu, X., Zhao, D.: Event-triggered reinforcement learning approach for unknown nonlinear continuous-time system. In: 2014 International Joint Conference on Neural Networks, pp. 3677–3684. IEEE Press, Beijing (2014)

    Chapter  Google Scholar 

  10. Vamvoudakis, K.G.: Event-triggered optimal adaptive control algorithm for continuous-time nonlinear systems. IEEE/CAA Journal of Automatica Sinica 1(3), 282–293 (2014)

    Article  Google Scholar 

  11. Chowdhary, G., Johnson, E.: Concurrent learning for convergence in adaptive control without persistency of excitation. In: 49th IEEE Conference on Decision and Control (CDC), pp. 3674–3679. IEEE Press, Atlanta (2010)

    Chapter  Google Scholar 

  12. Modares, H., Lewis, F.L., Naghibi-Sistani, M.B.: Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems. Automatica 50(1), 193–202 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dongbin Zhao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Zhao, D., Zhang, Q., Li, X., Kong, L. (2015). Event-Triggered H  ∞  Control for Continuous-Time Nonlinear System. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25393-0_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics