Adaptive learning with guaranteed stability for discrete-time recurrent neural networks

Abstract

To avoid unstable learning, a stable adaptive learning algorithm was proposed for discrete-time recurrent neural networks. Unlike the dynamic gradient methods, such as the backpropagation through time and the real time recurrent learning, the weights of the recurrent neural networks were updated online in terms of Lyapunov stability theory in the proposed learning algorithm, so the learning stability was guaranteed. With the inversion of the activation function of the recurrent neural networks, the proposed learning algorithm can be easily implemented for solving varying nonlinear adaptive learning problems and fast convergence of the adaptive learning process can be achieved. Simulation experiments in pattern recognition show that only 5 iterations are needed for the storage of a 15 × 15 binary image pattern and only 9 iterations are needed for the perfect realization of an analog vector by an equilibrium state with the proposed learning algorithm.

Keywords

recurrent neural networks / adaptive learning / nonlinear discrete-time systems / pattern recognition

References

[1] GuptaL., McAvoyM.. Investigating the prediction capabilities of the simple recurrent neural network on real temporal sequences[J]. Pattern Recognition, 2000, 33(12): 2075-2081

[2] GuptaL., McAvoyM., PhegleyJ.. Classification of temporal sequences via prediction using the simple recurrent neural network[J]. Pattern Recognition, 2000, 33(10): 1759-1770

[3] ParlosA. G., ParthasarathyS., AtiyaA. F.. Neuro-predictive process control using on-line controller adaptation [J]. IEEE Trans on Control Systems Technology, 2001, 9(5): 741-755

[4] ZhuQ. M., GuoL.. Stable adaptive neurocontrol for nonlinear discrete-time systems[J]. IEEE Trans on Neural Networks, 2004, 15(3): 653-662

[5] LeungC. S., ChanL. W.. Dual extended Kalman filtering in recurrent neural networks[J]. Neural Networks, 2003, 16(2): 223-239

[6] LiH.-r., GuS.-sheng.. A fast parallel algorithm for a recurrent neural network[J]. Acta Automatica Sinica, 2004, 30(4): 516-522

[7] MandicD. P., ChambersJ. A.. A normalised real time recurrent learning algorithm[J]. Signal Processing, 2000, 80(9): 1909-1916

[8] MandicD. P., ChambersJ. A.Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability[M], 2001, Chichester, John Wiley & Sons, Ltd

[9] WerbosP. J.. Backpropagation through time: What it does and how to do it[J]. Proc IEEE, 1990, 78(10): 1550-1560

[10] WilliamsR. J., ZipserD.. A learning algorithm for continually running fully recurrent neural networks[J]. Neural Computation, 1989, 1(2): 270-280

[11] AtiyaA. F., ParlosA. G.. New results on recurrent network training: Unifying the algorithms and accelerating convergence[J]. IEEE Trans on Neural Networks, 2000, 11(3): 697-709

[12] DengH., LiH.-xiong.. A novel neural network approximate inverse control for unknown nonlinear discrete dynamical systems[J]. IEEE Trans on Systems, Man and Cybernetics—Part B, 2005, 35(1): 115-123

[13] JinL., GuptaM. M.. Stable dynamic backpropagation learning in recurrent neural networks [J]. IEEE Trans on Neural Networks, 1999, 10(6): 1321-1334

[14] NarendraK. S., ParthasarathyK.. Gradient methods for the optimization of dynamical systems containing neural networks[J]. IEEE Trans on Neural Networks, 1991, 2(2): 252-262