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Zero-Sum Differential Game in Wheeled Mobile Robot Control

  • Zenon Hendzel
  • Paweł PenarEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 934)

Abstract

Zero-sum differential game is a combination optimum control method and solution \( H_{\infty } \) control problem. Its solutions are based on Bellman’s principle of optimality, for which the solution for nonlinear dynamic object is not available. In this case, approximation method based on actor-critic algorithms are used. One of the approximation method – SPIA [1] was applied in wheeled mobile robot tracking control problem and presented in the article. Numerical tests for the solution of the zero-sum differential game approximating algorithm were compared with the classical PD algorithm.

The obtained results confirm theoretical assumptions concerning the relationship between zero-sum differential game and \( H_{\infty } \) control problem.

Keywords

Differential game Optimal control Approximation dynamic programming 

References

  1. 1.
    Vamvoudakis, K.G., Lewis, F.L.: Online solution of nonlinear two-player zero-sum games using synchronous policy iteration. Int. J. Robust Nonlinear Control 22, 1460–1483 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Vamvoudakis, K.G., Lewis, F.L.: Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem. Automatica 46(5), 878–888 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Zhu, Y., et al.: Iterative adaptive dynamic programming for solving unknown nonlinear zero-sum game based on online data, pp. 1–12 (2016)Google Scholar
  4. 4.
    Van der Schaft, A.J.: L2-gain analysis of nonlinear systems and nonlinear state feedback H-infinity Control. IEEE Trans. Autom. Control 37(6), 770–784 (1992)CrossRefGoogle Scholar
  5. 5.
    Abu-Khalaf, M., et al.: Nonlinear H2/H-Infinity Constrained Feedback Control. Springer, London (2006)Google Scholar
  6. 6.
    Starr, A.W., Ho, Y.C.: Nonzero-sum differential games. J. Optim. Theory Appl. 3(3), 184–206 (1969)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, F.-Y., Zhang, H., Liu, D.: Adaptive dynamic programming: an introduction. IEEE Comput. Intell. Mag. 4(May), 39–47 (2009)CrossRefGoogle Scholar
  8. 8.
    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. The MIT Press, Cambridge (1998)zbMATHGoogle Scholar
  9. 9.
    Yasini, S., et al.: Online concurrent reinforcement learning algorithm to solve two-player zero-sum games for partially unknown nonlinear continuous-time systems. Int. J. Adapt. Control Signal Process. 22(4), 325–343 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Żylski, W.: Kinematic and Dynamic of a Wheeled Mobile Robot (in Polish). Rzeszow University of Technology, Rzeszow (1996)Google Scholar
  11. 11.
    Gierlak, P., Hendzel, Z.: Control of a Wheel and Manipulation Robot (in Polish) (2011)Google Scholar
  12. 12.
    Brogliato, B., et al.: Dissipative Systems Analysis and Control. Springer, London (2007)CrossRefGoogle Scholar
  13. 13.
    Wang, D., et al.: Event-based input-constrained nonlinear H-infinity state feedback with adaptive critic and neural implementation. Neurocomputing 214, 848–856 (2016)CrossRefGoogle Scholar
  14. 14.
    Yasini, S., et al.: Approximate dynamic programming for two-player zero-sum game related to H-infinity control of unknown nonlinear continuous-time systems. Int. J. Control Autom. Syst. 13(1), 99–109 (2014)CrossRefGoogle Scholar
  15. 15.
    Hendzel, Z., Penar, P.: Application of differential games in mechatronic control system. Int. J. Appl. Mech. Eng. 21(4), 867–878 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Rzeszow University of TechnologyRzeszówPoland

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