Maintaining good glycemic control is a daily challenge for people with type 1 diabetes. Insulin requirements are changing constantly due to many factors, such as levels of stress and physical activity. The basal insulin requirement also has a circadian rhythm, adding another level of complexity. Automating the adjustment of insulin dosing would result in improved glycemic control, as well as an improved quality of life by significantly reducing the burden on the patient. Building on our previous success of using run-to-run control for prandial insulin dosing (a strategy adapted from the chemical process industry), we show how this same framework can be used to adjust basal infusion profiles. We present a mathematical model of insulin-glucose dynamics which we augment in order to capture the circadian variation in insulin requirements. Using this model, we show that the run-to-run framework can also be successfully applied to adjust basal insulin dosing.