Direct adaptive regulation and robustness analysis for systems in Brunovsky form using a new Neuro-Fuzzy method

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical System definition, which uses the concept of Fuzzy Adaptive Systems (FAS) operating in conjunction with High Order Neural Network Functions (HONNFs). Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type fuzzy dynamical system (FDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states. The development is combined with a sensitivity analysis of the closed loop in the presence of modeling imperfections and provides a comprehensive and rigorous analysis of the stability properties of the closed loop system. Simulations illustrate the potency of the method and its applicability is tested on the well known benchmark “Inverted Pendulum”, where it is shown that our approach is superior to the case of simple Recurrent High Order Neural Networks (RHONNs).