Abstract
The paper presents an application of the Approximate Dynamic Programming algorithm in Globalised Dual Heuristic Dynamic Programming configuration in the tracking control problem of the wheeled mobile robot Pioneer 2-DX. The Globalised Dual Heuristic Dynamic Programming algorithm is realised in the form of two structures, the actor and the critic, that can be implemented in the form of any adaptive algorithm, e.g. Artificial Neural Networks. The actor generates the suboptimal control law, the critic approximates the value function and its difference with respect to the states, what is equal to evaluation of the realised control law. The discrete tracking control system is composed of the Globalised Dual Heuristic Dynamic Programming algorithm, the PD controller and the supervisory term, which structure derives from the stability analysis realised using the Lapunov stability theorem. The proposed control system works on-line and its performance was verified using the wheeled mobile robot Pioneer 2-DX.
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References
Barto, A.G., Sutton, R.S., Anderson, C.W.: Neuronlike Adaptive Elements that Can Solve Difficult Learning Control Problems. IEEE Trans. Syst., Man, Cybern. 13, 834–846 (1983)
Barto, A.G., Sutton, R.: Reinforcement Learning: an Introduction. MIT Press, Cambridge (1998)
Fairbank, M., Alonso, E., Prokhorov, D.: Simple and Fast Calculation of the Second-Oorder Gradients for Globalized Dual Heuristic Dynamic Programming in Neural Networks. IEEE Trans. Neural Netw. Learn. Syst. 23, 1671–1676 (2012)
Giergiel, J., Hendzel, Z., Zylski, W.: Modeling and Control of Wheeled Mobile Robots. (in Polish). WNT, Warsaw (2002)
Giergiel, J., Zylski, W.: Description of Motion of a Mobile Robot by Maggie’s Equations. J. Theoret. Appl. Mech. 43, 511–521 (2005)
Hendzel, Z.: An Adaptive Critic Neural Network for Motion Control of a Wheeled Mobile Robot. Nonlinear Dynam. 50, 849–855 (2007)
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)
Hendzel, Z., Szuster, M.: Discrete Neural Dynamic Programming in Wheeled Mobile Robot control. Commun Nonlinear Sci Numer Simulat. 16, 2355–2362 (2011)
Hendzel, Z., Szuster, M.: Heuristic Dynamic Programming in Wheeled Mobile Robot Control. In: 14th IFAC International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, pp. 37–41 (2009)
Liu, D., Wang, D., Yang, X.: An Iterative Adaptive Dynamic Programming Algorithm for Optimal Control of Unknown Discrete-Time Nonlinear Systems with Constrained Inputs. Inform Sciences 220, 331–342 (2013)
Miller, W.T., Sutton, R.S., Werbos, P.J. (eds.): Neural Networks for Control. MIT Press, Cambridge (1990)
Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality. Willey-Interscience, Princeton (2007)
Prokhorov, D., Wunch, D.: Adaptive Critic Designs. IEEE T Neural Networ 8, 997–1007 (1997)
Si, J., Barto, A.G., Powell, W.B., Wunsch, D.: Handbook of Learning and Approximate Dynamic Programming. IEEE Press, Wiley-Interscience, New York (2004)
Syam, R., Watanabe, K., Izumi, K.: Adaptive Actor-Critic Learning for the Control of Mobile Robots by Applying Predictive Models. Soft Computing 9, 835–845 (2005)
Venayagamoorthy, G.K., Wunsch, D.C., Harley, R.G.: Adaptive Critic Based Neurocontroller for Turbogenerators with Global Dual Heuristic Programming. In: IEEE Power Engineering Society Winter Meeting 1, pp. 291–294. IEEE Press, New York (2000)
Wang, D., Liu, D., Wei, Q., et al.: Optimal Control of Unknown Nonaffine Nonlinear Discrete-Time Systems Based on Adaptive Dynamic Programming. Automatica 48, 1825–1832 (2012)
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Szuster, M. (2014). Globalised Dual Heuristic Dynamic Programming in Tracking Control of the Wheeled Mobile Robot. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8468. Springer, Cham. https://doi.org/10.1007/978-3-319-07176-3_26
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DOI: https://doi.org/10.1007/978-3-319-07176-3_26
Publisher Name: Springer, Cham
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