Stability of a novel iterative learning control scheme with adaptive filtering

This paper presents theoretical investigations into the stability property of novel approach, which circumvents a classic tradeoff between robustness and performance in iterative learning control (ILC). The tradeoff is usually performed by designing an appropriate filtering mechanism to compensate for non-perfect resetting and noise. Time-frequency analysis is used to examine the frequency content of error signals over the compact time support of the reference signal. This then allows the filter to effectively change its bandwidth as a function of time thereby allowing high frequency system dynamics to enter into the learning process at the appropriate time instants. At the same time, robustness is maintained by reducing the bandwidth of the filter when the system dynamics do not exhibit high frequency characteristics so as to attenuate the effect of noise on the learning stability. This adaptive Q-filter iterative learning controller is needed for systems that have non-smooth nonlinearities. Its advantages are demonstrated with successful simulations and experiments in the authors´ earlier publications [2001] [2002]. In this paper, a theoretical study utilizing repetitive control and switching control theories shows that the control action of the proposed adaptive Q-filter ILC will be BIBO stable.