Skip to main content

Online Iterative Adaptive Dynamic Programming Approach for Solving the Zero-Sum Game for Nonlinear Continuous-Time Systems with Partially Unknown Dynamics

  • Conference paper
  • First Online:
Proceedings of 2022 International Conference on Autonomous Unmanned Systems (ICAUS 2022) (ICAUS 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 1010))

Included in the following conference series:

  • 74 Accesses

Abstract

The current study presents an online iterative adaptive dynamic programming approach to resolve the zero-sum game (ZSG) for nonlinear continuous-time (CT) systems containing a partially unknown dynamic. The Hamilton-Jacobian-Issacs (HJI) equation is solved along the state trajectory according to the value function approximation and the policy improvement online. Relaxed dynamic programming is utilized to ensure the algorithm’s convergence. Model and costate networks were established to conduct the method. Computational simulations are performed to present the efficiency of the algorithm.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 709.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 899.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 899.99
Price excludes VAT (USA)
  • Durable hardcover 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

Similar content being viewed by others

References

  1. Sutton, R.S., Barto, A.G.: Reinforcement learning: an introduction. IEEE Trans. Neural Networks 9(5), 1054 (1998)

    Article  Google Scholar 

  2. Lewis, F., Vrabie, D., Vamvoudakis, K.: Reinforcement learning and feedback control: using natural decision methods to design optimal adaptive controllers. IEEE Control Syst. 32(6), 76–105 (2012)

    Google Scholar 

  3. Song, R., Lewis, F.L., Wei, Q., Zhang, H.: Off-policy actor-critic structure for optimal control of unknown systems with disturbances. IEEE Trans. Cybern. 46(5), 1041–1050 (2016)

    Article  Google Scholar 

  4. Khan, S.G., Herrmann, G., Lewis, F.L., Pipe, T., Melhuish, C.: Reinforcement learning and optimal adaptive control: an overview and implementation examples. Annu. Rev. Control. 36(1), 42–59 (2012)

    Article  Google Scholar 

  5. Vrabie, D., Lewis, F.: Adaptive Dynamic Programming algorithm for finding online the equilibrium solution of the two-player zero-sum differential game. In: Proceedings of the International Joint Conference on Neural Networks (2010)

    Google Scholar 

  6. 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  MathSciNet  MATH  Google Scholar 

  7. Yasini, S., Sistani, M.B.N., Karimpour, A.: Approximate dynamic programming for two-player zero-sum game related to H control of unknown nonlinear continuous-time systems. Int. J. Control. Autom. Syst. 13(1), 99–109 (2014)

    Article  Google Scholar 

  8. Su, H., Zhang, H., Zhang, K., Gao, W.: Online reinforcement learning for a class of partially unknown continuous-time non-linear systems via value iteration. Optim. Control Appl. Methods 39(2), 1011–1028 (2018)

    Article  MATH  Google Scholar 

  9. Rantzer, A.: Relaxed dynamic programming in switching systems. IEE Proc. - Control Theory Appl. 153(5), 567–574 (2006)

    Article  MathSciNet  Google Scholar 

  10. Lincoln, B., Rantzer, A.: Relaxing dynamic programming. IEEE Trans. Automat. Contr. 51(8), 1249–1260 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, D., Liu, D.: Neuro-optimal control for a class of unknown nonlinear dynamic systems using SN-DHP technique. Neurocomputing 121, 218–225 (2013)

    Article  Google Scholar 

  12. Zhang, H., Qin, C., Luo, Y.: Neural-network-based constrained optimal control scheme for a discrete-time switched nonlinear system using dual heuristic programming, IEEE Trans. Autom. Sci. Eng. 11(3), 839–849, 2014

    Google Scholar 

  13. Andrade, G.A., Da Fonseca Neto, J.V., Helena, P., Márcio, M.R., Gonsalves, E.: RLS estimator state space basis for the solution of HJB-Riccati Equation in approximate dynamic programming. In: IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 3, no. PART 1, pp. 1153–1160 (2014)

    Google Scholar 

  14. Xiao, G., Zhang, H., Zhang, K., Wen, Y.: Value iteration based integral reinforcement learning approach for H∞ controller design of continuous-time nonlinear systems. Neurocomputing 285, 51–59 (2018)

    Article  Google Scholar 

  15. Sun, J., Liu, C.: Finite-horizon differential games for missile–target interception system using adaptive dynamic programming with input constraints. Int. J. Syst. Sci. 49(2), 264–283 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Lewis, F.L., Vrabie, D.: Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits Syst. Mag. 9(3), 32–50 (2009)

    Article  Google Scholar 

  17. Zhu, Y., Zhao, D., Li, X.: Iterative adaptive dynamic programming for solving unknown nonlinear zero-sum game based on online data. IEEE Trans. Neural Networks Learn. Syst. 28(3), 714–725 (2016)

    Article  MathSciNet  Google Scholar 

  18. Liu, D., Li, H., Wang, D.: Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm. Neurocomputing 110, 92–100 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hang Guo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Beijing HIWING Sci. and Tech. Info Inst

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fu, B., Sun, B., Guo, H., Yang, T., Fu, W. (2023). Online Iterative Adaptive Dynamic Programming Approach for Solving the Zero-Sum Game for Nonlinear Continuous-Time Systems with Partially Unknown Dynamics. In: Fu, W., Gu, M., Niu, Y. (eds) Proceedings of 2022 International Conference on Autonomous Unmanned Systems (ICAUS 2022). ICAUS 2022. Lecture Notes in Electrical Engineering, vol 1010. Springer, Singapore. https://doi.org/10.1007/978-981-99-0479-2_262

Download citation

Publish with us

Policies and ethics