Output based direct adaptive iterative learning control for nonlinear systems

In this paper, an output based direct adaptive iterative learning controller using a fuzzy neural network is proposed for a class of uncertain repeatable nonlinear systems. As we assume that the states are not measurable, a sliding window of measurements is introduced to design the iterative learning controller without state observer. Based on a derived error model, a fuzzy neural network using sliding window of measurement is introduced to design a fuzzy neural learning component. It is used to overcome the design difficulty in dealing with the certainty equivalent controller. On the other hand, an averaging filter approach is adopted to design a robust learning component. It will compensate for the uncertainties due to fuzzy neural approximation error, input disturbance and state estimation errors. A Lyapunov like analysis is applied to show that all the adjustable parameters as well as internal signals remain bounded for all iterations. Furthermore, the norm of output tracking error will asymptotically converge to a tunable residual set as iteration goes to infinity.