A new Neuro-Fuzzy method for direct adaptive control of unknown nonlinear systems with robustness analysis

The direct adaptive regulation of affine in the control nonlinear square (system states equals to control inputs) dynamical systems 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 Dynamical Systems (FDS) operating in conjunction with High Order Neural Network Functions, which in the sequel approximate the fuzzy rules. This way the unknown plant is modeled by a fuzzy-recurrent high order neural network (F-RHONN), which is of known structure considering the neglected nonlinearities. 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. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating law. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks where it is shown that our approach is superior to the case of simple RHONN´s.