Impulsive control systems have shown strong potential to represent and address challenging problems, especially in the biomedical field. In recent research, these problems have been tackled with advances in linear impulsive control systems. However, many biomedical applications are better described by nonlinear impulsive models, and therefore, it is necessary to develop analysis tools and control strategies in this context. In the literature, the main properties of nonlinear impulsive control systems have been fully understood, but there is no major development of control strategies. Particularly, there is no substantiation of model predictive control (MPC) strategies maintaining convexity of the optimization problem and closed-loop stability, and there is no control strategy to reduce the offset problem when there are parameter variations, which is a common situation in biological processes. Therefore, the main novelties of this paper are: (i) an MPC formulation extended to nonlinear impulsive systems that addresses non-zero tracking, (ii) the sufficient and necessary conditions to guarantee the stability of the closed-loop system at an equilibrium target, (iii) a comprehensive description of an offset-free MPC to handle low to moderate plant-model mismatches, (iv) the conditions to guarantee offset-free control. Finally, the MPC and offset-free MPC are tested to address the drug administration problem in two biomedical applications: oncolytic virus therapy, to regulate tumor dynamics using doses of oncolytic, and type 1 diabetes treatment, to regulate glycemia using insulin injections. Satisfactory results were obtained in simulation scenarios including parameter variations in nonlinear models that represent the corresponding dynamics.
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