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Reinforcement Learning in Discrete Neural Control of the Underactuated System

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7894))

Abstract

The article presents a new approach to the problem of a discrete neural control of an underactuated system, using reinforcement learning method to an on-line adaptation of a neural network. The controlled system is of the ball and beam type, which is the nonlinear dynamical object with the number of control signals smaller than the number of degrees of freedom. The main part of the neural control system is the actor-critic structure, that comes under the Neural Dynamic Programming algorithms family, realised in the form of Dual Heuristic Dynamic Programming structure. The control system includes moreover the PD controller and the supervisory therm, derived from the Lyapunov stability theorem, that ensures stability. The proposed neural control system works on-line and does not require a preliminary learning. Computer simulations have been conducted to illustrate the performance of the control system.

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References

  1. Barto, A.G., Sutton, R.S., Anderson, C.W.: Neuronlike Adaptive Elements that Can Solve Difficult Learning Control Problems. IEEE Transactions on Systems, Man and Cybernetics 13, 834–846 (1983)

    Article  Google Scholar 

  2. Blajer, W., Kolodziejczyk, K.: Contol of Underactuated Mechanical Systems with Servo-Constraints. Nonlinear Dynamics 50, 781–791 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eaton, P.H., Prokhorov, D.V., Wunsch, D.C.: Neurocontroller Alternatives for Fuzzy Ball-and-Beam Systems With Nonuniform Nonlinear Friction. IEEE Transactions on Neural Networks and Learning Systems 11, 423–435 (2000)

    Article  Google Scholar 

  4. Burghardt, A., Giergiel, J.: Modelling and Control of an Underactuated Sphere and Beam System. Communications in Nonlinear Science and Numerical Simulation 16, 2350–2354 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hendzel, Z., Burghardt, A.: Adaptive Neural Network Control of Underactuated System. In: 4th International Conference on Neural Computation Theory and Applications, pp. 505–509. SciTePress, Barcelona (2012)

    Google Scholar 

  6. Hendzel, Z., Szuster, M.: Discrete Model-Based Dual Heuristic Programming in Wheeled Mobile Robot Control. In: 10th International Conference on Dynamical Systems - Theory and Applications, Lodz, pp. 745–752 (2009)

    Google Scholar 

  7. Hendzel, Z., Szuster, M.: Discrete Model-Based Adaptive Critic Designs in Wheeled Mobile Robot Control. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 264–271. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Keshmiri, M., Jahromi, A.F., Mohebbi, A., Amoozgar, M.H., Xie, W.F.: Modeling and Control of Ball and Beam System Using Model Based and Non-model Based Control Approaches. International Journal on Smart Sensing and Intelligent Systems 5, 14–35 (2012)

    Google Scholar 

  9. Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality. Wiley Interscience, Princeton (2007)

    Book  Google Scholar 

  10. Prokhorov, D., Wunch, D.: Adaptive Critic Designs. IEEE Transactions on Neural Networks 8, 997–1007 (1997)

    Article  Google Scholar 

  11. Si, J., Barto, A.G., Powell, W.B., Wunsch, D.: Handbook of Learning and Approximate Dynamic Programming. IEEE Press, Wiley-Interscience (2004)

    Google Scholar 

  12. Spong, M.W.: Modeling and control of elastic joint robot. Journal of Dynamic Systems, Measurement, and Control 109, 310–319 (1987)

    Article  MATH  Google Scholar 

  13. Spong, M.W.: Underactuated Mechanical Systems. In: Siciliano, B., Valavanis, K.P. (eds.) Control Problems in Robotics and Automation. LNCIS, vol. 230, pp. 135–150. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Wen, Y.: Nonlinear PD Regulation for Ball and Beam System. International Journal of Electrical Engineering Education 46, 59–73 (2009)

    Article  Google Scholar 

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Hendzel, Z., Burghardt, A., Szuster, M. (2013). Reinforcement Learning in Discrete Neural Control of the Underactuated System. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-38658-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38657-2

  • Online ISBN: 978-3-642-38658-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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