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Multi-period repetitive learning control for a class of unmatched systems with unknown control direction

In this work, we propose a new method approach of designing a repetitive learning controller for a class of unmatched nonlinear systems with both completely unknown virtual control coefficients and unknown time-varying parameters. By incorporating a Nussbaum-type function and backstepping technique, the learning control mechanism is constructed with both differential and difference updating learning laws. The design method does not require a priori knowledge of the control direction. By applying Lyapunov-Krasovskii functional, it is proved that the proposed learning control scheme can guarantee uniform ultimate boundedness of the states. Furthermore, the control performance can be achieved by an appropriate choice of the design parameters. A simulation example is given to illustrate the effectiveness of the proposed approach