Adaptive fuzzy control for non-linear dynamical systems based on differential flatness theory

A new approach to adaptive fuzzy control for uncertain non-linear dynamical systems, is proposed. The considered class of systems can be written in the Brunovsky (canonical) form after a transformation of their state variables and control input. The resulting control signal is shown to consist of non-linear elements, which in case of unknown system parameters can be approximated using neurofuzzy networks. An adaptation law for the neurofuzzy approximators can be computed using Lyapunov stability analysis. It is shown that the proposed adaptation law assures stability of the closed loop. Simulation experiments on benchmark non-linear dynamical systems are used to evaluate the performance of the proposed flatness-based adaptive fuzzy control scheme.