Adaptive iterative learning control for high-order nonlinear systems with random initial state shifts

Aiming at the tracking problem for a class of high-order nonlinear systems with arbitrary initial state, this paper proposes different initial state shifts rectifying schemes for systems with different orders from the perspective of solving differential equations to ensure that the systems achieve complete tracking over the specified interval. This method relaxes the requirement of initial positioning in iterative learning control, and solves the problem of iterative learning control for high-order nonlinear systems with arbitrary initial state error. The theoretical analysis shows that the proposed schemes can make all signals in the system bounded, and ensure that the tracking error in the preset interval tends to zero as the number of iterations increases. When designing the controller, the arctangent function is used to avoid flutter of the control signal and related variables. The final simulations verify the effectiveness of the proposed algorithms.