Design of Cycles by Impulsive Feedback: Application to Discrete Dosing

The task of maintaining a predefined level of effect in a dynamical plant by applying periodic control actions often arises in, e.g., process control and medicine. When the state variables of the plant represent the concentrations of chemical substances and the control action constitutes an instantaneous introduction of a certain quantity of a chemical or drug, this control setup is referred to as a (discrete) dosing problem. The present article examines an amplitude- and frequency-modulated impulsive controller that, under stationary conditions, generates a desired sequence of uniform and equidistant control impulses based on continuous measurements of the output of a smooth positive nonlinear time-invariant single-input single-output plant with Wiener structure. The controller design method is based on constructing and stabilizing the fixed point of a discrete map that describes the evolution of the state vector of the continuous plant between successive impulsive control action instants. Stability of the fixed point ensures the existence of a basin of attraction around the stationary trajectory, where solutions of the closed-loop system converge to the stationary solution after perturbation. The convergence rate is determined by the slopes of the amplitude and frequency modulation functions of the impulsive controller. The proposed controller is applied to dosing of the drug atracurium in closed-loop neuromuscular blockade (NMB), and its performance is evaluated on a database of patient-specific pharmacokinetic (PK)-pharmacodynamic (PD) models estimated from clinical data. It is demonstrated that an implementation of the standard regimen as a pulse-modulated feedback controller significantly reduces the incidence of underdosing events.