A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper

paying special attention to the analysis of the model order problem. The method uses a neuro-fuzzy (NF) modeling of the unknown system

which combines fuzzy systems (FSs) with high order neural networks (HONNs). We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS)

which

however

may assume a smaller number of states than the original unknown model. The omission of states

referred to as a model order problem

is modeled by introducing a disturbance term in the approximating equations. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. An adaptive modification method

termed ‘parameter hopping’

is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured. The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’

where it is shown that it performs quite well under a reduced model order assumption. Moreover

the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).