Offset-free MPC strategy for nonzero regulation of linear impulsive systems

In various biomedical applications, drug administration treatment can be modeled as an impulsive control system. Despite the development of different control strategies for impulsive systems, the elimination of the offset generated by a plant-model mismatch has not yet been researched. In biomedical systems, this mismatch is a consequence of physiological changes and can result in inaccurate treatment of patients. Therefore, control techniques that accomplish the objectives by compensating the effect of variations are required. The present paper proposes and substantiates a novel offset-free model predictive control (MPC) strategy for impulsive systems. To that aim, an impulsive disturbance model is introduced, and an observer design is developed that includes new observability criteria for estimating the disturbance and the state. Further, it is demonstrated that the proposed control strategy achieves zero offset tracking from an analysis of the observer and the controller at steady state. Additionally, the controller incorporates a recent MPC formulation to steer the state to an equilibrium set using artificial/intermediary variables to achieve nonzero regulation. Finally, these results are evaluated and illustrated using a dynamical model for type 1 diabetic patients.