  In this paper we provide provable regret guarantees for an online
meta-learning receding horizon control algorithm in an iterative control
setting. We consider the setting where, in each iteration the system to be
controlled is a linear deterministic system that is different and unknown, the
cost for the controller in an iteration is a general additive cost function and
there are affine control input constraints. By analysing conditions under which
sub-linear regret is achievable, we prove that the meta-learning online
receding horizon controller achieves an average of the dynamic regret for the
controller cost that is $\tilde{O}((1+1/\sqrt{N})T^{3/4})$ with the number of
iterations $N$. Thus, we show that the worst regret for learning within an
iteration improves with experience of more iterations, with guarantee on rate
of improvement.
