An initial state learning method for iterative learning control of uncertain time-varying systems

In iterative learning control (ILC), a common assumption is that the initial states in each repetitive operation should be inside a given ball centred at the desired initial states which may be unknown. This assumption is critical to the stability analysis and the size of the ball will directly affect the final output trajectory tracking errors. In this paper, this assumption is removed by using an initial state learning scheme together with the traditional D-type ILC updating law. Both linear and nonlinear time-varying uncertain systems are investigated. Uniform bounds for the final tracking errors are obtained and these bounds are only dependent on the system uncertainties and disturbances, yet independent of the initial errors. Furthermore, the desired initial states can be identified through learning iterations.