A combined adaptive law for fuzzy iterative learning control of nonlinear systems with varying control tasks

To deal with the iterative control of uncertain nonlinear systems with varying control tasks, nonzero initial resetting state errors, and nonrepeatable mismatched input disturbance, a new adaptive fuzzy iterative learning controller is proposed in this paper. The main structure of this learning controller is constructed by a fuzzy learning component and a robust learning component. For the fuzzy learning component, a fuzzy system used as an approximator is designed to compensate for the plant nonlinearity. For the robust learning component, a sliding-mode-like strategy is applied to overcome the nonlinear input gain, input disturbance, and fuzzy approximation error. Both designs are based on a time-varying boundary layer which is introduced not only to solve the problem of initial state errors but also to eliminate the-possible undesirable chattering behavior. A new adaptive law combining time- and iteration-domain adaptation is derived to search for suitable values of control parameters and then guarantee the closed-loop stability and error convergence. This adaptive algorithm is designed without using projection or deadzone mechanism. With a suitable choice of the weighting gain, the memory size for the storage of parameter profiles can be greatly reduced. It is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. Moreover, the norm of tracking state error vector will asymptotically converge to a tunable residual set even when the desired tracking trajectory is varying between successive iterations.