Direct adaptive control of unknown multi-variable nonlinear systems with robustness analysis using a new neuro-fuzzy representation and a novel approach of parameter hopping

The direct adaptive regulation of affine in the control nonlinear 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 (F-HONNFs). Since the actual plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate HONNFs. 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 proposed scheme does not require a-priori information from the expert on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence 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 where it is shown that the proposed approach is superior to the case of simple RHONN's.