Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.