Nonlinear system modeling with dynamic adaptive neuro-fuzzy inference system

This paper introduces the architecture and learning procedure of dynamic adaptive neuro-fuzzy inference system (DANFIS) for nonlinear dynamical system modeling. In our DANIS model, IF part of the rules are comprised of Gaussian type membership functions and THEN part of the rules are differential equations of linear functions. In order to find optimal model parameters, a gradient based algorithm Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used. Gradients in this algorithm is calculated by using adjoint sensitivity method. To validate the model, two simulations, Van der Pol oscillator and tunnel diode circuit, are performed. Simulation results are also given to demonstrate the effectiveness of the proposed DANFIS with learning method.