Based on sparsity maximization we propose a controller for Multiple Daily Injections (MDI)therapy for Type 1 Diabetes melitus (T1DM) individuals. Based on convex relaxations onthe sparsity maximization problems and by implementing personalised linear models of pa-tient we formulate a model predictive controller to determine insulin boluses. By relaxingthe constraints of the unsafe regions after meal consumption for pre-defined time interval weobtain sufficient performance with a long enough horizon. To improve the controllers perfor-mance a case-based reasoning framework is implemented to tune the controller constraintsfor increasing time spent in euglycemia.