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

This paper presents a novel training algorithm for computationally intellig ent architectures, whose outputs are differentiable with respect to the adj ustable design parameters. The algorithm combines the gradient descent tech nique with the variable-structure-systems approach. The combination is perf ormed by expressing the conventional weight update rule in continuous time and application of sliding-mode control method to the gra- dient-based trai ning procedure. The proposed combination therefore exhibits a degree of rob ustness with respect to the unmodeled multivariable internal dynamics of gr adient descent and to the environmental disturbances, With conventional tra ining procedures, the excitation of this dynamics during a training cycle c an lead to instability, which may be difficult to alleviate due to the mult idimensionality of the solution space and the ambiguities on the free desig n parameters, such as learning rate or momentum coefficient. This paper dev elops 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 (par ameter stabilization) while minimizing an appropriate cost function (cost o ptimization), 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 multilay er perceptron, In order to demonstrate the robustness of the approach prese nted, a considerable amount of observation noise and varying payload condit ions are also studied.