On stability of nonzero set-point for nonlinear impulsive control systems

D'JORGE, AGUSTINA; ANDERSON, ALEJANDRO; FERRAMOSCA, ANTONIO; GONZÁLEZ, ALEJANDRO HERNÁN; ACTIS, MARCELO

SYSTEMS AND CONTROL LETTERS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2022 vol. 165

0167-6911

The interest in non-linear impulsive systems (NIS) has been growing due to their impact on applicationproblems such as disease treatments (diabetes, HIV, influenza, COVID-19, among many others), wherethe control action (drug administration) is given by short-duration pulses followed by time periodsof null values. Within this framework, the concept of equilibrium needs to be extended (redefined)to allow the system to keep orbiting (between two consecutive pulses) in some state-space sets outof the origin, according to the usual objectives of most real applications. Although such sets can becharacterized by means of a discrete-time system obtained by sampling the NIS at the impulsivetimes, no agreement has been reached on their asymptotic stability (AS) under optimizing controlstrategies. This paper studies the asymptotic stability of control equilibrium orbits for NIS, based on theunderlying discrete-time system, in order to establish the conditions under which the AS for the latterleads to the AS for the former. Furthermore, based on the latter AS characterization, an impulsive ModelPredictive Control (i-MPC) that feasibly stabilizes the non-linear impulsive system is presented. Thebiomedical problems of intravenous bolus administration of Lithium and antiretrovirals administrationfor HIV treatments are considered as simulation examples to demonstrate the controller performance