An observer-based model reference adaptive iterative learning controller for nonlinear systems without state measurement

In this paper, an observer-based model reference adaptive iterative learning control strategy using a filtered fuzzy neural network is proposed for more general class of uncertain nonlinear systems. Since the system states are not measurable, a state tracking error observer is introduced for state estimation. Based on the state tracking error observer, a model reference adaptive control technique using a mixed time-domain and s-domain technique is presented to derive an output observation error model. In this error model, the unknown system nonlinearities become a kind of uncertain sources to a known, stable and relative degree one linear system. It is further transformed into a new formulation by an averaging filter and some auxiliary signals so that the iterative learning controller can be implemented without using differentiators. The main learning component which performs as an system approximator is constructed by a filtered fuzzy neural network using the estimated state variables as the network input. To overcome the lumped uncertainties from function approximation error and state estimation error, a normalization signal is applied as a bounding function to design a robust learning component. Besides, a stabilization learning component is used to guarantee the boundedness of internal signals. Since the optimal parameters for a good function approximation are in general unavailable, adaptive algorithms are derived to search for suitable parameters during each iteration. We show that all the adjustable parameters as well as internal signals remain bounded for all iterations. The norm of output tracking error will asymptotically converge to a tunable residual set whose size depends on some design parameters of averaging filter. A practical ball and beam system is given to verify the nice tracking performance of the proposed learning scheme.