A new direct adaptive regulator with robustness analysis of systems in Brunovsky form

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro-fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. 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 laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).