Stabilizing and robustifying the learning mechanisms of artificial neural networks in control engineering applications

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Abstract
This paper discusses the stabilizability of artificial neural networks trained by utilizing the gradient information. The method proposed constructs a dynamic model of the conventional update mechanism and derives the stabilizing values of the learning rate. The stability in this context corresponds to the convergence in adjustable parameters of the neural network structure. It is shown that the selection of the learning rate as imposed by the proposed algorithm results in stable training in the sense of Lyapunov. Furthermore, the algorithm devised filters out the high frequency dynamics of the gradient descent method. The excitation of this dynamics typically occurs in the presence of noise and abruptly changing the parameters of the mapping being learned. This adversely influences the learning performance that can be attained during a training cycle. A natural consequence following this excitation is divergence in parameter space. The method analyzed in this paper integrates the gradient descent technique with variable structure systems methodology, which is well known for its robustness to environmental disturbances. In the simulations, control of a three degrees of freedom anthropoid robot is chosen for the evaluation of the performance. For this purpose, a feedforward neural network structure is utilized as the controller. Highly nonlinear dynamics of the plant, existence of a considerable amount of observation noise, and the adverse effects of gravitational forces constitute the difficulties to be alleviated by the neurocontroller trained with the proposed method. In order to come up with a fair comparison, the results obtained with the pure gradient descent technique with the same initial conditions are also presented and discussed. © 2000 John Wiley & Sons, Inc.