Theory of iterative learning control system interconnection

Abstract

In this research, we study an interconnection of two general iterative learning control (ILC) system. This topic is a new topic in the area of ILC. To develop this theory, a new robustness notion describing t he effect of disturbance and initial condition in ILC system is introduced. This new notion is called iterative input to state stability (iterative ISS), which is formulated following t he idea of input to state stability. Based on this notion, the cascade and feedback interconnection of ILC system is considered. It is proved that bounded disturbance bounded state property and disturbance asymptotic gain property hold for feedback and cascade system interconnection, provided each subsystem is iterative ISS. In order to see the applicability of the theory of ILC system interconnection, we perform a case study. In particular, we choose a certain class of nonlinear adaptive Lyapunov based ILC and investigate whether iterative ISS is a property of this class of control system. If iterative ISS can be derived from this particular adaptive nonlinear ILC then the general ILC system theory interconnection is applicable to this class of nonlinear adaptive ILC. The result shows that nonlinear adaptive ILC does not have the property of iterative ISS although under restrictive disturbance and initial condition set. As a recommendation for future work, we discuss a possibility to achieve the iterative ISS property of this class of nonlinear adaptive ILC.

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