An adaptive terminal iterative learning control for nonaffine nonlinear discrete-time systems

A new adaptive terminal iterative learning controller is presented in this paper for nonaffine nonlinear discrete-time systems with iteration-varying desired terminal output and random initial system output. A terminal output tracking error model is firstly derived by using the system function and the differential mean value theorem since it is assumed only system terminal output is measurable. Based on the derived terminal output tracking error model, an iteration-varying boundary layer and a dead-zone like auxiliary terminal error are proposed to design an adaptive terminal iterative learning controller. The iterative learning controller and the width of boundary layer are updated from trial to trial in order to compensate for an unknown nominal desired terminal input and an unknown uncertain desire terminal input respectively. Based on a Lyapunov like analysis, we show that the boundedness of control input, system output and width of boundary layer are guaranteed for each iteration and each time instant. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.