Adaptive iterative learning control of non-uniform trajectory tracking for strict feedback nonlinear time-varying systems with unknown control direction

The iterative learning control problem of strict feedback nonlinear system with unknown time-varying parameters and uncertain control direction is an open problem. An iterative learning control strategy is presented for a class of nonlinear time-varying systems with unknown control direction to solve the non-uniform trajectory tracking problem. Backstepping design technique is applied to deal with system dynamics with non-global Lipschitz nonlinearities. Based on the Lyapunov-like synthesis, we show that all signals in the closed-loop system remain bounded over a pre-specified time interval [0,T][0,T], and complete non-uniform trajectory tracking of the system output is achieved. The time-varying parameters are expanded into Fourier series with bounded remained term. A typical series is introduced in order to deal with the unknown bound of remained term and the non-uniform trajectory tracking. Nussbaum function is used to deal with unknown control direction. Finally, a simulation example shows the feasibility and effectiveness of the approach.