Stable indirect adaptive fuzzy-neuro control for a class of nonlinear systems

The paper presents an indirect adaptive fuzzy-neuro control scheme for a general high-order nonlinear continuous system. In the proposed scheme a fuzzy-neuro controller constructed based on the fuzzy neural networks for approximating the unknown nonlinearities of dynamic systems, and a sliding mode controller constructed to compensate for the modelling errors of fuzzy neural networks are incorporated. The parameters of the fuzzy neural networks are modified using the recently proposed fuzzy-neuro algorithms named Online Sequential Fuzzy Extreme Learning Machine (OS-Fuzzy-ELM), where the parameters of the membership functions characterizing the linguistic terms in the if-then rules are assigned randomly. However different from the original OS-Fuzzy-ELM algorithm, the consequent parameters of if-then rules are updated based on the Lyapunov synthesis approach to guarantee the stability of the overall control system, even in the presence of modelling errors which are offset using the sliding mode controller. Finally the proposed adaptive fuzzy-neuro controller is applied to control the inverted pendulum system where two different reference trajectories are tracked and the simulation results demonstrate a good track performance is achieved by the proposed control scheme.