An observer-based fuzzy neural network adaptive ILC for nonlinear systems

To deal with the iterative learning control problem for more general class of uncertain nonlinear systems using only output measurement, an observer based adaptive iterative learning control strategy using filtered fuzzy neural network was proposed in this paper. A model reference control technique is firstly presented to derive a state error observer for state estimation. A mixed time-domain and s -domain representation is then used to develop an error model as a relative degree one stable system with some uncertain nonlinearities and filtered signals as the inputs. An averaging filter is also proposed to further transform the error model so that the AILC can be implemented without using differentiators. The main learning component of the controller is constructed by an filtered fuzzy neural network with the estimated state variables as network input. This main component performs as an approximator to compensate for the unknown system nonlinearities. Furthermore, a normalization signal is applied as a bounding function for designing a robust learning component in order to overcome the lumped uncertainties from function approximation error and state estimation error. Finally, a stabilization learning component is used to guarantee the boundedness of internal signals. Adaptive algorithms are derived to search for suitable parameters during each iteration since the optimal parameters for a good function approximation are in general unavailable. Based on a Lyapunov like analysis, we show that the output tracking error can converge, with all the internal signals bounded, to a small residual set whose level of magnitude depends on a design parameter. Simulation results also show the nice tracking performance with application to some practical nonlinear systems.