Identification and Adaptive Control of Dynamic Nonlinear Systems Using Sigmoid Diagonal Recurrent Neural Network

ABSTRACT

The goal of this paper is to introduce a new neural network architecture called Sigmoid Diagonal Recurrent Neural Network (SDRNN) to be used in the adaptive control of nonlinear dynamical systems. This is done by adding a sigmoid weight victor in the hidden layer neurons to adapt of the shape of the sigmoid function making their outputs not restricted to the sigmoid function output. Also, we introduce a dynamic back propagation learning algorithm to train the new proposed network parameters. The simulation results showed that the (SDRNN) is more efficient and accurate than the DRNN in both the identification and adaptive control of nonlinear dynamical systems.

The goal of this paper is to introduce a new neural network architecture called Sigmoid Diagonal Recurrent Neural Network (SDRNN) to be used in the adaptive control of nonlinear dynamical systems. This is done by adding a sigmoid weight victor in the hidden layer neurons to adapt of the shape of the sigmoid function making their outputs not restricted to the sigmoid function output. Also, we introduce a dynamic back propagation learning algorithm to train the new proposed network parameters. The simulation results showed that the (SDRNN) is more efficient and accurate than the DRNN in both the identification and adaptive control of nonlinear dynamical systems.

KEYWORDS

Sigmoid Diagonal Recurrent Neural Networks, Dynamic Back Propagation, Dynamic Nonlinear Systems, Adaptive Control

Sigmoid Diagonal Recurrent Neural Networks, Dynamic Back Propagation, Dynamic Nonlinear Systems, Adaptive Control

Cite this paper

nullT. Aboueldahab and M. Fakhreldin, "Identification and Adaptive Control of Dynamic Nonlinear Systems Using Sigmoid Diagonal Recurrent Neural Network,"*Intelligent Control and Automation*, Vol. 2 No. 3, 2011, pp. 176-181. doi: 10.4236/ica.2011.23021.

nullT. Aboueldahab and M. Fakhreldin, "Identification and Adaptive Control of Dynamic Nonlinear Systems Using Sigmoid Diagonal Recurrent Neural Network,"

References

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[5] L. Chen and K. S. Narendra, “Nonlinear Adaptive Control Using Neural Networks and Multiple Models,” Proceedings of the 2000 American Control Conference, Chicago, 2002, pp. 4199-4203.

[6] R. Zhan and J. Wan “Neural Network-Aided Adaptive Unscented Kalman Filter for Nonlinear State Estimation,” IEEE Signal Processing Letters, Vol. 13, No. 7, 2006, pp. 445-448. doi:10.1109/LSP.2006.871854

[7] A. S. Poznyak, W. Yu, E. N. Sanchez and J. P. Perez, “Nonlinear Adaptive Trajectory Tracking Using Dynamic Neural Networks,” IEEE Transactions on Neural Networks, Vol. 10, No. 6, 1999, pp. 1402-1411. doi:10.1109/72.809085

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[10] Xiang Li, Z. Q. Chen and Z. Z. Yuan, “Simple Recurrent Neural Network-Based Adaptive Predictive Control for Nonilnear Systems,” Asian Journal of Control, Vol. 4, No. 2, June 2002, pp. 231-239.

[11] N. Kumar , V. Panwar, N. Sukavanam, S. P. Sharma and J. H. Borm, “Neural Network-Based Nonlinear Tracking Control of Kinematically Redundant Robot Manipulators,” Mathematical and Computer Modelling, Vol. 53, No. 9-10, 2011, pp. 1889-1901. doi:10.1016/j.mcm.2011.01.014

[12] J. Pedro and O. Dahunsi, “Neural Network Based Feedback Linearization Control of a Servo-Hydraulic Vehicle Suspension System,” International Journal of Applied Mathematics and Computer Science, Vol. 21, No. 1, 2011, pp. 137-147. doi:10.2478/v10006-011-0010-5

[13] A. Thammano and P. Ruxpakawong, “Nonlinear Dynamic System Identification Using Recurrent Neural Network with Multi-Segment Piecewise-Linear Connection Weight,” Memetic Computing, Vol. 2, No. 4, 2010, pp. 273-282. doi:10.1007/s12293-010-0042-7

[14] A. C Tsoi and A. D. Back, “Locally Recurrent Globally Feedforward Networks: A Critical Review of Architectures,” IEEE Transaction Neural Networks, Vol. 5, No. 2, 1994, pp. 229-239. doi:10.1109/72.279187

[15] T. Rashid, B. Q. Huang and T. Kechadi, “Auto-Regressive Recurrent Neural Network Approach for Electricity Load Forecasting,” International Journal of Computational Intelligence, Vol. 3, No. 1, 2007, pp.66-71.

[16] B. A. Pearlmutter, “Gradient Calculations for Dynamic Recurrent Neural Networks: A Survey,” IEEE Transactions on Neural Networks, Vol. 6, No. 5, 1995, pp. 1212-1228. doi:10.1109/72.410363

[1] A. U. Levin, and K. S. Narendra, “Control of Nonlinear Dynamical Systems Using Neural Networks—Part II: Observability, Identification and Control,” IEEE Transactions on Neural Networks, Vol. 7, No. 1, 1996, pp. 30-42. doi:10.1109/72.478390

[2] C. C. Ku and K. Y. Lee, “Diagonal Recurrent Neural Networks for Dynamic System Control,” IEEE Transactions on Neural Networks, Vol. 6, No. 1, 1995, pp. 144-156. doi:10.1109/72.363441

[3] G. L. Plett, “Adaptive Inverse Control of Linear and Nonlinear Systems Using Dynamic Neural Networks,” IEEE Transactions on Neural Networks, Vol. 14, No.2, 2003, pp. 360-376. doi:10.1109/TNN.2003.809412

[4] K. S. Narendra and K. Parthasarathy, “Identification and Control of Dynamical Systems Using Neural Networks,” IEEE Transactions on Neural Networks, Vol. 1, No. 1, 1990, pp. 4-27. doi:10.1109/72.80202

[5] L. Chen and K. S. Narendra, “Nonlinear Adaptive Control Using Neural Networks and Multiple Models,” Proceedings of the 2000 American Control Conference, Chicago, 2002, pp. 4199-4203.

[6] R. Zhan and J. Wan “Neural Network-Aided Adaptive Unscented Kalman Filter for Nonlinear State Estimation,” IEEE Signal Processing Letters, Vol. 13, No. 7, 2006, pp. 445-448. doi:10.1109/LSP.2006.871854

[7] A. S. Poznyak, W. Yu, E. N. Sanchez and J. P. Perez, “Nonlinear Adaptive Trajectory Tracking Using Dynamic Neural Networks,” IEEE Transactions on Neural Networks, Vol. 10, No. 6, 1999, pp. 1402-1411. doi:10.1109/72.809085

[8] P. A. Mastorocostas, “A Constrained Optimization Algorithm for Training Locally Recurrent Globally Feedforward Neural Networks,” Proceedings of International Joint Conference on Neural Networks, Montreal, 31 July 4 August 2005, pp.717-722.

[9] A. Tarek, “Improved Design of Nonlinear Controllers Using Recurrent Neural Networks,” Master Dissertation, Cairo University, 1997.

[10] Xiang Li, Z. Q. Chen and Z. Z. Yuan, “Simple Recurrent Neural Network-Based Adaptive Predictive Control for Nonilnear Systems,” Asian Journal of Control, Vol. 4, No. 2, June 2002, pp. 231-239.

[11] N. Kumar , V. Panwar, N. Sukavanam, S. P. Sharma and J. H. Borm, “Neural Network-Based Nonlinear Tracking Control of Kinematically Redundant Robot Manipulators,” Mathematical and Computer Modelling, Vol. 53, No. 9-10, 2011, pp. 1889-1901. doi:10.1016/j.mcm.2011.01.014

[12] J. Pedro and O. Dahunsi, “Neural Network Based Feedback Linearization Control of a Servo-Hydraulic Vehicle Suspension System,” International Journal of Applied Mathematics and Computer Science, Vol. 21, No. 1, 2011, pp. 137-147. doi:10.2478/v10006-011-0010-5

[13] A. Thammano and P. Ruxpakawong, “Nonlinear Dynamic System Identification Using Recurrent Neural Network with Multi-Segment Piecewise-Linear Connection Weight,” Memetic Computing, Vol. 2, No. 4, 2010, pp. 273-282. doi:10.1007/s12293-010-0042-7

[14] A. C Tsoi and A. D. Back, “Locally Recurrent Globally Feedforward Networks: A Critical Review of Architectures,” IEEE Transaction Neural Networks, Vol. 5, No. 2, 1994, pp. 229-239. doi:10.1109/72.279187

[15] T. Rashid, B. Q. Huang and T. Kechadi, “Auto-Regressive Recurrent Neural Network Approach for Electricity Load Forecasting,” International Journal of Computational Intelligence, Vol. 3, No. 1, 2007, pp.66-71.

[16] B. A. Pearlmutter, “Gradient Calculations for Dynamic Recurrent Neural Networks: A Survey,” IEEE Transactions on Neural Networks, Vol. 6, No. 5, 1995, pp. 1212-1228. doi:10.1109/72.410363