Stable training of computationally intelligent systems by using variable structure systems technique

This paper presents a novel training algorithm for computationally intelligent architectures, whose outputs are differentiable with respect to the adjustable design parameters. The algorithm combines the gradient descent technique with the variable-structure-systems approach. The combination is performed by expressing the conventional weight update rule in continuous time and application of sliding-mode control method to the gra- dient-based training procedure. The proposed combination therefore exhibits a degree of robustness with respect to the unmodeled multivariable internal dynamics of gradient descent and to the environmental disturbances, With conventional training procedures, the excitation of this dynamics during a training cycle can lead to instability, which may be difficult to alleviate due to the multidimensionality of the solution space and the ambiguities on the free design parameters, such as learning rate or momentum coefficient. This paper develops a heuristic that a computationally intelligent system, which may be a neural network architecture or a fuzzy inference mechanism, can be trained such that the adjustable pa- rameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization), The proposed approach is applied to the control of a robotic arm in two different ways. In one, a standard fuzzy system architecture is used, whereas in the second, the arm is controlled by the use of a multilayer perceptron, In order to demonstrate the robustness of the approach presented, a considerable amount of observation noise and varying payload conditions are also studied.