Iterative Learning Control for Linear Continuous-time Systems with Vector Relative Degree under Varying Trail Length

This note considers the problem of iterative learning control (ILC) for a class of linear continuous-time multiple-input multiple-output (MIMO) systems with vector relative degree, where the trail length of control input is different from that of system state and output for a specific iteration. An iteration-average operator is included in the proposed ILC law to address the varying trail lengths. The proposed ILC algorithm allows that the control input length is iteration-varying during the ILC process, and can achieve desired trajectory tracking at control time interval. A numerical example is carried out to illustrate the effectiveness of the proposed ILC scheme.