On stabilization of gradient-based training strategies for computationally intelligent systems

This paper develops a novel training methodology for computationally intelligent systems utilizing gradient information in parameter updating. The devised scheme uses the first-order dynamic model of the training procedure and applies the variable structure systems approach to control the training dynamics. This results in an optimal selection of the learning rate, which is continually updated as prescribed by the adopted strategy. The parameter update rule is then mixed with the conventional error backpropagation method in a weighted average. The paper presents an analysis of the imposed dynamics, which is the response of the training dynamics driven solely by the inputs designed by variable structure control approach. The analysis continues with the global stability proof of the mixed training methodology and the restrictions on the design parameters. The simulation studies presented are focused on the advantages of the proposed scheme with regards to the compensation of the adverse effects of the environmental disturbances and its capability to alleviate the inherently nonlinear behavior of the system under investigation. The performance of the scheme is compared with that of a conventional backpropagation. It is observed that the method presented is robust under noisy observations and time varying parameters due to the integration of gradient descent technique with variable structure systems methodology. In the application example studied, control of a two degrees of freedom direct-drive robotic manipulator is considered. A standard fuzzy system is chosen as the controller in which the adaptation is carried out only on the defuzzifier parameters.