Robust Neural Network Tracking Controller Using Simultaneous Perturbation Stochastic Approximation

This paper considers the design of robust neural network tracking controllers for nonlinear systems. The neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to establish a robust neural control system, with guaranteed boundedness for both the input/output (I/O) signals and the weights of the neural network. The neural network is trained by the simultaneous perturbation stochastic approximation (SPSA) method instead of the standard backpropagation (BP) algorithm. The proposed neural control system guarantees closed-loop stability of the estimation system, and a good tracking performance. The performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts, fast convergence, and robustness against system disturbance.

[1]  Marios M. Polycarpou,et al.  Automated fault diagnosis in nonlinear multivariable systems using a learning methodology , 2000, IEEE Trans. Neural Networks Learn. Syst..

[2]  Q. Song,et al.  Robust neural network controller for variable airflow volume system , 2002 .

[3]  J. Spall.  Multivariate stochastic approximation using a simultaneous perturbation gradient approximation , 1992 .

[4]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[5]  Qing Song,et al.  Dynamic pruning algorithm for multilayer perceptron based neural control systems , 2006, Neurocomputing.

[6]  James C. Spall,et al.  A neural network controller for systems with unmodeled dynamics with applications to wastewater treatment , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[7]  V. R. Cluett,et al.  Robustness Analysis of Discrete-Time Adaptive Control Systems Using Input-Output Stability Theory: a , 1988 .

[8]  Marios M. Polycarpou,et al.  Learning and convergence analysis of neural-type structured networks , 1992, IEEE Trans. Neural Networks.

[9]  J. Spall,et al.  Model-free control of nonlinear stochastic systems with discrete-time measurements , 1998, IEEE Trans. Autom. Control..

[10]  Jie Huang,et al.  Neural-Network-Based Approximate Output Regulation of Discrete-Time Nonlinear Systems , 2007, IEEE Transactions on Neural Networks.

[11]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[12]  Qing Song,et al.  Robust backpropagation training algorithm for multilayered neural tracking controller , 1999, IEEE Trans. Neural Networks.

[13]  Michael G. Safonov,et al.  Stability and Robustness of Multivariable Feedback Systems , 1980 .

[14]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[15]  Sylvain Contassot-Vivier,et al.  Basins of attraction in fully asynchronous discrete-time discrete-state dynamic networks , 2006, IEEE Transactions on Neural Networks.

[16]  F. Lewis,et al.  Discrete-time neural net controller for a class of nonlinear dynamical systems , 1996, IEEE Trans. Autom. Control..

[17]  E. Chong,et al.  A deterministic analysis of stochastic approximation with randomized directions , 1998, IEEE Transactions on Automatic Control.

[18]  Hassan K. Khalil,et al.  Adaptive control of a class of nonlinear discrete-time systems using neural networks , 1995, IEEE Trans. Autom. Control..

[19]  Michael J. Grimble,et al.  Robust multivariable implicit self-tuning control , 1993 .

[20]  Fuchun Sun,et al.  Stable neural-network-based adaptive control for sampled-data nonlinear systems , 1998, IEEE Trans. Neural Networks.

[21]  R. Ortega,et al.  Robustness of discrete-time direct adaptive controllers , 1985 .

[22]  Qing Song,et al.  Robust adaptive fault accommodation for a robot system using a radial basis function neural network , 2001 .

[23]  R.R. Mohler,et al.  Stability and robustness of multivariable feedback systems , 1981, Proceedings of the IEEE.

[24]  Laxmidhar Behera,et al.  On Adaptive Learning Rate That Guarantees Convergence in Feedforward Networks , 2006, IEEE Transactions on Neural Networks.

[25]  Alexander G. Loukianov,et al.  Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks , 2007, IEEE Transactions on Neural Networks.

[26]  Pratibha Mishra,et al.  Advanced Engineering Mathematics , 2013 .

[27]  Qing Song.  A Robust Information Clustering Algorithm , 2005, Neural Computation.

[28]  Alfonso García-Cerezo,et al.  An input-output based robust stabilization criterion for neural-network control of nonlinear systems , 2001, IEEE Trans. Neural Networks.

[29]  Liu Sheng,et al.  A Normalized Adaptive Training of Recurrent Neural Networks With Augmented Error Gradient , 2008, IEEE Transactions on Neural Networks.