Output Corridor Impulsive Control of First-order Continuous System with Non-local Attractivity Analysis

TL;DR

This paper develops an impulsive control method for linear systems to keep outputs within a specified corridor, with applications in chemical kinetics and medicine dosing.

Contribution

It introduces a novel impulsive control design for hybrid systems, ensuring local and global attractivity of a stable periodic solution within a predefined corridor.

Findings

Successfully designed a 1-cycle stable solution for the control problem.

Established conditions for local and global attractivity of the 1-cycle.

Numerical example demonstrates application to intravenous paracetamol dosing.

Abstract

This paper addresses the design of an impulsive controller for a continuous scalar time-invariant linear plant that constitutes the simplest conceivable model of chemical kinetics. The model is ubiquitous in process control as well as pharmacometrics and readily generalizes to systems of Wiener structure. Given the impulsive nature of the feedback, the control problem formulation is particularly suited to discrete dosing applications in engineering and medicine, where both doses and inter-dose intervals are manipulated. Since the feedback controller acts at discrete time instants and employs both amplitude and frequency modulation, whereas the plant is continuous, the closed-loop system exhibits hybrid dynamics featuring complex nonlinear phenomena. The problem of confining the plant output to a predefined corridor of values is considered. The method at the heart of the proposed approach is to design a stable periodic solution, called a 1-cycle, whose one-dimensional orbit coincides with the predefined corridor. Conditions ensuring local and global attractivity of the 1-cycle are established. As a numerical illustration of the proposed approach, the problem of intravenous paracetamol dosing is considered.