A novel optimization procedure for training of fuzzy inference systems by combining variable structure systems technique and Levenberg-Marquardt algorithm

This paper presents a novel training algorithm for fuzzy inference systems. The algorithm combines the Levenberg-Marquardt algorithm with variable structure systems approach. The combination is performed by expressing the parameter update rule in continuous time and application of sliding mode control method to the gradient based training procedure. The proposed combination therefore exhibits a degree of robustness to the unmodeled multivariable internal dynamics of Levenberg-Marquardt technique. 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 concerning the environmental conditions. This paper proves that a fuzzy inference mechanism can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization). In the application example, control of a two degrees of freedom direct drive SCARA robotic manipulator is considered. As the controller, a standard fuzzy system architecture is used and the parameter tuning is performed by the proposed algorithm.