Abstract
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.
Highlights
I MPULSIVE Control Systems (ICSs) are a class of systems in which the input action has a short duration in comparison with the sampling time and the dynamics of the system itself
The main merits of this work are listed as follows: 1) An model predictive control (MPC) formulation for nonlinear ICS is developed based on the zone MPC (ZMPC) that uses (i) an equilibrium artificial reference as a new decision variable, (ii) a dynamic cost function that penalizes the deviation to the artificial equilibrium, and (iii) a final cost function to steer the artificial variable to the actual target set
The first developed scheme is a ZMPC with artificial reference variables, with which it is ensured that at each time step the controller computes a control action that brings the state to an equilibrium inside the target
Summary
I MPULSIVE Control Systems (ICSs) are a class of systems in which the input action has a short duration in comparison with the sampling time and the dynamics of the system itself. 3) From the literature review, offset-free MPC strategies for linear and nonlinear discrete-time systems have been found These cover different approaches with and without a state estimator, robust and adaptable formulations. The main merits of this work are listed as follows: 1) An MPC formulation for nonlinear ICS is developed based on the ZMPC that uses (i) an equilibrium artificial reference as a new decision variable, (ii) a dynamic cost function that penalizes the deviation to the artificial equilibrium, and (iii) a final cost function to steer the artificial variable to the actual target set This strategy has the advantage of allowing the inclusion of a target set instead of a set-point, and it ensures feasibility under any change of the target.
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