Advertisement

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

  • Dongbin Zhao
  • Qichao Zhang
  • Xiangjun Li
  • Lingda Kong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Basar, T., Olsder, G.J., Clsder, G.J., et al.: Dynamic noncooperative game theory. Academic Press, London (1995)MATHGoogle Scholar
  2. 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)MathSciNetCrossRefGoogle Scholar
  3. 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.2014.2348991Google Scholar
  4. 4.
    Alippi, C., Ferrero, A., Piuri, V.: Artificial intelligence for instruments and measurement applications. IEEE Instrumentation & Measurement Magazine 1(2), 9–17 (1998)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 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)MathSciNetCrossRefGoogle Scholar
  7. 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)MathSciNetCrossRefGoogle Scholar
  8. 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. 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)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

<SimplePara><Emphasis Type="Bold">Open Access</Emphasis> This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. </SimplePara> <SimplePara>The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.</SimplePara>

Authors and Affiliations

  • Dongbin Zhao
    • 1
  • Qichao Zhang
    • 1
  • Xiangjun Li
    • 2
  • Lingda Kong
    • 2
  1. 1.State Key Laboratory of Management and Control for Complex Systems, Institute of AutomationChinese Academy of SciencesBeijingChina
  2. 2.China Electric Power Research InstituteBeijingChina

Personalised recommendations