Sample-data adaptive iterative learning control for a class of unknown nonlinear systems

Using a technique of sampled-data transformation for differentiation and integration, a sampled-data adaptive iterative learning control is presented for a class of nonlinear systems. The main control structure is designed by a fuzzy system used as a function approximator to compensate for an unknown certainty equivalent controller. The robustness problem due to function approximation error and input disturbance is solved by a technique of time-varying boundary layer which is utilized to construct an auxiliary error function for adaptive law design. Stability and convergence of the learning system is proved via a Lyapunov-like analysis if the adaptation gains satisfy a convergence condition. Since the convergence condition depends on the upper bound of system unknown input/output coupling function, an identifier based on fuzzy system design is further proposed to estimate the unknown bound. The adaptive laws for the fuzzy parameters are investigated to guarantee that identification error will asymptotically converge to zero. Finally, a numerical example is given to demonstrate the effectiveness of the iterative learning control system.