Convergence evaluation of optimization-based stochastic iterative learning control

This paper deals with the convergence analysis and evaluation of iterative learning control (ILC) against stochastic disturbances. By minimizing the trace of the covariance matrix of the output tracking error, an optimization-based design method is proposed for stochastic ILC, from which the monotonic convergence of the output tracking error is established in the mean square sense. Moreover, the fastest convergence rate at the order O(1/k) is achieved for both the output tracking and input updating errors in stochastic ILC. Particularly, a notion of stochastic learnability is presented for the input updating process, by which a unified analysis framework to simultaneously address output tracking and input updating problems in stochastic ILC is developed. Simulation tests on a mobile robot are performed to verify the effectiveness of our optimization-based stochastic ILC results.