Derivation of a parameter stabilizing training criterion for adaptive neuro-fuzzy inference systems in motion control

This paper presents a novel training algorithm for adaptive neuro-fuzzy inference systems. The algorithm combines the error back-propagation algorithm with the variable structure systems approach. Expressing the parameter update rule as a dynamic system in continuous time and applying sliding mode control (SMC) methodology to the dynamic model of the gradient based training procedure results in the parameter stabilizing part of training algorithm. The proposed combination therefore exhibits a degree of robustness to the unmodelled multivariable internal dynamics of the gradient-based training algorithm. With conventional training procedures, the excitation of this dynamics during a training cycle can lead to instability, which may be difficult to alleviate owing to the multidimensionality of the solution space and the ambiguities concerning the environmental conditions. This paper shows that a neuro-fuzzy model can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization), which is based on state tracking performance. In the application example, trajectory control of a two degrees of freedom direct drive robotic manipulator is considered. As the controller, an adaptive neuro-fuzzy inference mechanism is used and, in the parameter tuning, the proposed algorithm is utilized.