Repetitive learning control for bilinear parametric systems with unknown time-varying delays and time-varying parameters

An repetitive learning control strategy is presented for a class of bilinear parametric systems with mixed unknown time-varying and time-invariant parameters and unknown time varying delay. By reconstructing the system equation, the time-varying delay is combined into an unknown periodic time-varying vector which is estimated by a periodic adaptive mechanism. The proposed control scheme includes a differential-difference mixed-type adaptive law used to estimate the unknown time-varying parameters and an adaptive repetitive learning control. Based on the Lyapunov-Krasovskii energy function synthesis, we show that all signals in the closed-loop system remain bounded and the asymptotic convergence of the tracking error. The simulation results show the feasibility and effectiveness of the approach.