Abstract: The direct adaptive regulation for ane in the control nonlinear dynamical systems possessing unknown nonlinearities, is considered in this pa- per. The method is based on a new Neuro-Fuzzy Dynamical System denition, which uses the concept of Fuzzy Dynamical Systems (FDS) operating in con- junction with High Order Neural Network Functions (F-HONNFs). Since the plant is considered unknown, we rst 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. The fuzzy-recurrent high order neural networks (F-RHONN) are used as models of the unknown plant, practically transforming the original unknown system into a F-RHONN model which is of known structure, but contains a number of unknown constant value parameters. The proposed scheme does not require a-priori experts' information on the num- ber and type of input variable membership functions making it less vulnerable to initial design assumptions, is extremely fast and, hence, can be applied in several dicult and very demanding real-time engineering applications. When the F-RHONN model matches the unknown plant, we provide a comprehensive and rigorous analysis of the stability properties of the closed loop system. Con- vergence of the state to zero plus boundedness of all other signals in the closed loop is guaranteed without the need of parameter (weights) convergence, which is assured only if a suciency-of-excitation condition is satised. The existence of the control signal is always assured by introducing a novel method of param- eter hopping and incorporating it in weight updating law. Simulations illustrate the approximation superiority of the proposed scheme in comparison to other well established approaches. The applicability of the method is also tested on well known simulated nonlinear plants where it is shown that by following the proposed procedure one can obtain asymptotic regulation. Comparison is also made to simple RHONN controllers, showing that our approach is superior to the case of simple RHONN's.

Abstract: The indirect adaptive regulation of unknown non-linear dynamical systems is considered m this paper. Tne method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.