Model Predictive Control for Linear Impulsive Systems

Linear impulsive control systems have been extensively studied with respect to their equilibrium points which, in most cases, are no other than the origin. However, the trajectory of an impulsive system cannot be stabilized to arbitrary desired points hindering their utilization in a great many applications. In this technical note, we study the equilibrium of linear impulsive systems with respect to target-sets. We properly extend the notion of invariance and design stabilizing model predictive controllers (MPC). Finally, we apply the proposed methodology to control the intravenous bolus administration of Lithium.