Robust adaptive iterative learning control for nonrepetitive systems with iteration-varying parameters and initial state

This paper explores how to construct an adaptive iteration learning control (AILC) mechanism for a class of discrete-time nonrepetitive systems subject to iteration-varying unknown parameters and unidentical initial condition. Firstly, for the linear discrete-time nonrepetitive systems, by minimizing the discrepancy of the real system outputs from the estimated system outputs, a gradient-type adaptation law is designed to estimate the system lower triangular parameter matrix and the system initial state. Especially, the current parametric estimation is updated by virtue of the input-output data and the previous estimation. Secondly, an AILC mechanism is constructed based on the estimated system lower triangular parameter matrix, where the control input algorithm and the adaptation law are scheduled in an interactive mode. Thirdly, the boundedness of the estimation error between the real system matrix and the estimation one is derived by means of vector norm theory. Based on the boundedness of the estimation error, the robust condition of the proposed AILC is given. Finally, the proposed AILC is investigated for a class of nonlinear affine systems and the corresponding results are captured. Simulation results illustrate the validity and effectiveness of the proposed AILC schemes.