MPC with State Window Target Control in Linear Impulsive Systems

In this paper a zone MPC controller is proposed to deal with the tracking problem of linear impulsive control systems. The control strategy is based on the analysis of some system equilibrium generalizations, which are characterized by means of two underlying discrete-time systems. First, it is shown that the impulsive system has a kind of orbits in the state space, passing trough the equilibrium points of the underlying systems, and then, these geometric equilibrium entities (the orbits) are used as possible targets for a zone control system. Based on this new description, an efficient MPC algorithm is designed to steer the system to a set - usually associated to a «therapeutic window» in drug administration problems - that includes a previously defined family of orbits. The strategy is tested by controlling an impulsive model of an intravenous bolus administration of Lithium ions system.