Stable Adaptive Neural Control of a Robot Arm
Affiliation(s)
Université Le Havre—GREAH, Lebon, Le Havre, France. Al Baha University, Al Baha, Saudi Arabia.
Université Le Havre—GREAH, Lebon, Le Havre, France. Al Baha University, Al Baha, Saudi Arabia.
ABSTRACT
In this paper, stable indirect adaptive control with recurrent neural networks (RNN) is presented for square multivariable non-linear plants with unknown dynamics. The control scheme is made of an adaptive instantaneous neural model, a neural controller based on fully connected “Real-Time Recurrent Learning” (RTRL) networks and an online parameters updating law. Closed-loop performances as well as sufficient conditions for asymptotic stability are derived from the Lyapunov approach according to the adaptive updating rate parameter. Robustness is also considered in terms of sensor noise and model uncertainties. This control scheme is applied to the manipulator robot process in order to illustrate the efficiency of the proposed method for real-world control problems.
In this paper, stable indirect adaptive control with recurrent neural networks (RNN) is presented for square multivariable non-linear plants with unknown dynamics. The control scheme is made of an adaptive instantaneous neural model, a neural controller based on fully connected “Real-Time Recurrent Learning” (RTRL) networks and an online parameters updating law. Closed-loop performances as well as sufficient conditions for asymptotic stability are derived from the Lyapunov approach according to the adaptive updating rate parameter. Robustness is also considered in terms of sensor noise and model uncertainties. This control scheme is applied to the manipulator robot process in order to illustrate the efficiency of the proposed method for real-world control problems.
Cite this paper
S. Zerkaoui and S. Badran, "Stable Adaptive Neural Control of a Robot Arm," Intelligent Control and Automation, Vol. 3 No. 2, 2012, pp. 140-145. doi: 10.4236/ica.2012.32016.
S. Zerkaoui and S. Badran, "Stable Adaptive Neural Control of a Robot Arm," Intelligent Control and Automation, Vol. 3 No. 2, 2012, pp. 140-145. doi: 10.4236/ica.2012.32016.
References
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[1] W. D. Chang, “Robust Adaptive Single Neural Control for a Class of Uncertain Nonlinear Systems with Input Nonlinearity,” Information Sciences, Vol. 171, No. 1-3, 2005, pp. 261-271. doi:10.1016/j.ins.2004.05.001 [2] J. Wang, “Sensitivity Identification Enhanced Control Strategy for Nonlinear Process Systems,” Computers & Chemical Engineering, Vol. 27, No.11 , 2003, pp. 16311640. doi:10.1016/S0098-1354(03)00117-0 [3] F. Fourati, M. Chtourou and M. Kamoun, “Stabilization of Unknown Nonlinear Systems Using Neural Networks,” Applied Soft Computing, Vol. 8, No. 2, 2008, pp. 11211130. doi:10.1016/j.asoc.2007.04.002 [4] D. Wang and P. Bao, “Enhancing the Estimation of Plant Jacobian for Adaptive Neural Inverse Control,” Neurocomputing, Vol. 34, No. 1-4, 2000, pp. 99-115. doi:10.1016/S0925-2312(00)00319-2 [5] S. S. Ge and C. Wang, “Direct Adaptive NN Control of a Class of Nonlinear Systems,” IEEE Transactions on Neural Networks, Vol. 13, No. 1, 2002, pp. 214-221. [6] W. Gao and R. R. Selmic, “Neural Network Control of a Class of Nonlinear Systems With Actuator Saturation,” IEEE Transactions on Neural Networks, Vol. 17, No. 1, 2003, pp. 147-156. [7] J. M. Renders, M. Saerens and H. Bersini, “Adaptive Neurocontrol of MIMO Systems Based on Stability Theory,” IEEE Colloquium on Advances in Neural Networks for Control and Systems, Orlando, 25-27 May 1994, pp. 2476-2481. [8] S. S. Ge, C. C. Hang and T. Zhang, “Stable Adaptive Control for Multivariable Nonlinear Systems with a Triangular Control Structure,” IEEE Transactions on Automatic Control, Vol. 45, No. 6, 2000, pp. 1221-1225. [9] S. S. Ge, C. Wang and Y. H. Tan, “Adaptive Control of Partially Known Nonlinear Multivariable Systems Using Neural Networks,” IEEE International Symposium on Proceedings of the Intelligent Control, Mexico City, 5-7 September 2001, pp. 292-297. [10] L. Tian and C. Collins, “A Dynamic Recurrent Neural Network-Based Controller for a Rigid-Flexible Manipulator System,” Mechatronics, 2004, Vol. 14, No. 5, pp. 471-490. doi:10.1016/j.mechatronics.2003.10.002 [11] S. Zerkaoui, F. Druaux, E. Leclercq and D. Lefebvre, “Indirect Neural Control for Plant-wide Systems: Application to the Tennessee Eastman Challenge Process,” Computers and Chemical Engineering, Vol. 34, No. 2, 2009, pp. 232-243. doi:10.1016/j.compchemeng.2009.08.003 [12] R. J. Williams and D. Zipser, “A Learning Algorithm for Continually Running Fully Recurrent Neural Networks,” Neural Computation, Vol. 1, No. 2, 1989, pp.270-280. doi:10.1162/neco.1989.1.2.270 [13] E. Leclercq, F. Druaux, D. Lefebvre and S. Zerkaoui, “Autonomous Learning Algorithm for Fully Connected Recurrent Networks,” Neurocomputing, Vol. 63, 2005, pp. 25-44. doi:10.1016/j.neucom.2004.04.007 [14] R. M., Sanner and J.-J. E., Slotine, “Gaussian Networks for Direct Adaptive Control,” IEEE Transactions on Neural Networks, Vol. 3, No. 6, 1992, pp. 837-863. [15] D. Wang and P. Bao, “Enhancing the Estimation of Plant Jacobian for Adaptive Neural Inverse Control,” Neurocomputing, Vol. 34, No. 1-4, 2000, pp. 99-115. doi:10.1016/S0925-2312(00)00319-2 [16] H. R. Wu and M. Palaniswami, “An Adaptive Tracking Controller Using Neural Networks for a Class of Nonlinear Systems,” IEEE Transactions on Neural Networks, Vol. 9, No. 5, 1998, pp. 947-955. doi:10.1109/72.712168 [17] S. Zerkaoui, F. Druaux, E. Leclercq and D. Lefebvre, “Commande Adaptative par Réseau de Neurones HyperConnectés: Etude de la Stabilité et de la Robustesse,” Journées Doctorales en Modélisation, Analyse et Conduite des Systèmes Dynamiques, Lyon, 5-7 September 2005, Article ID: 024. [18] S. Zerkaoui, F. Druaux, E. Leclercq and D. Lefebvre, “Stable Adaptive Control with Recurrent Neural Networks,” International Federation of Automatic Control, Prague, 4-8 July 2005, Article ID: 02103. [19] S. Zerkaoui, F. Druaux, E. Leclercq and D. Lefebvre, “Robust Stability Analysis for Indirect Neural Adaptive Control,” International Control Conference, Glasgow, 30 August-1 September 2006, Article ID: 105. [20] S. Zerkaoui, F. Druaux, E. Leclercq and D. Lefebvre, “Multivariable Adaptive Control for Non-Linear Systems: Application to the Tennessee Eastman Challenge Process,” European Control Conference, Kos, 2007. [21] R. Chaumont, E. Vasselin, M. Gorka and D. Lefebvre, “Forward Kinematics and Geometric Control of a Medical Robot: Application to Dental Implants,” International Conference on Informatics in Control, Automation and Robotics, Angers, 9-11 May 2007, pp. 110-115.