Contraction Analysis of Nonlinear Iterative Learning Control

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Journal Article
IFAC-PapersOnLine, 2017, 50, (1), pp. 10876-10881
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Iterative learning control (ILC) is widely used as a simple method for precise tracking of systems under repetitive conditions. ILC operates by “learning” from the previous iteration's errors, correcting them over a number of iterations. However, the question of whether or not a nonlinear ILC system converges is still in general an open one. Assuming a state-space formulation, we use contraction analysis to formulate a convergence condition for ILC system as a linear matrix inequality (LMI). Finally, we compute a convergence certificate for a simple example involving “anticogging” a permanent-magnet synchronous motor driving a pendulum in simulation.
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