Lyapunov stability analysis in the training of type 2 neuro-fuzzy inference system with a hybrid algorithm based on gradient descent and Kalman filter

The stability of the training process in the identification of nonlinear systems is one of the foremost issues in control research. This paper studies the training stability of an interval type 2 adaptive neuro-fuzzy Inference system (IT2ANFIS) as an identifier through a newfound Lyapunov function. Lyapunov stability analysis is conducted on the training of IT2ANFIS, when the premise and the consequent of the system are trained with the gradient descent algorithm and the Kalman Filter, respectively. Therefore, using the proposed stability analysis, the permissible limits for the adjustable parameters of the algorithms are applied to the algorithms to maintain the stability of the identification process. According to the stability analysis of this study, wide ranges of adaptive limits are obtained for the adjustable parameters of the algorithms. Besides, the simulation results show that when the permissible limits are chosen based on the proposed stability analysis, the identification process is stable with acceptable performance. The proposed method outperforms other methods in terms of root mean square error, simulation time, and its less stagnation in the trap of local minimums when it is utilized in the training of the Mackey-Glass chaotic time series and a nonlinear plant with stochastic data sets.