Convergence analysis of adaptive tuning parameter for robust stabilizing control of $N$-level quantum systems

This paper analyzes how the weight function affects the properties of convergence: where and how fast the estimate converges. Stabilization control of quantum systems has been getting much attention as research in quantum information technology progresses, and of course, it is necessary to consider uncertainties in practice. In order to deal with a large uncertain quantum system, we recently proposed an adaptive parameter tuning algorithm based on the study of robust stabilization of
$N$
-level quantum systems by Liang, Amini, and Mason (SIAM J. Control Optim., 59(1), 669–692, 2021). In this paper, we briefly review our proposed method and analyze its convergence performance of the estimated parameter. The convergence analysis shows that certain conditions on the weight function are necessary for proper tuning, and the asymptotic convergence rate depends on only the choice of the function.