Partial-period adaptive repetitive control by symmetry

This paper presents a partial-period adaptive repetitive control method for a class of periodically time-varying nonlinear systems. To reduce the size of memory usage, the symmetric feature of periodic parameters is explored to form partial-period adaptation mechanisms. Both Half- and quarter-period adaptation strategies are proposed, and characterized analytically. The stability of the closed-loop system with each repetitive control is established, along with tracking error convergence to zero. In addition, the saturated-adaptation is suggested for providing bounded estimation.