Computing control invariant sets for waiting-time switched systems: A study case of glucose regulation

PEREZ, MARA ISABEL; ANDERSON, ALEJANDRO; ABUIN, PABLO; HERNANDEZ VARGAS, ESTEBAN ABELARDO; GONZÁLEZ, ALEJANDRO HERNÁN; ACTIS, MARCELO

IEEE Control Systems Letters

IEEE

Año: 2023

2475-1456

Waiting-time constraints, bounding the minimumand maximum time of permanence in a given mode ofa switched system, can be included in optimization-basedcontrol formulations by means of hard constraints. However,basic concepts such as equilibrium and invariancesets are modified by these constraints affecting the formalstability analysis as well. This paper explores general regionsof the state space wherein switched system trajectoriesunder waiting-time constraints can feasibly (and indefinitely)remain inside, replacing the concept of invariancewith those of permanence. Explicit algorithms to computethese regions inside an (out of the origin) target windoware provided, while the glucose regulation problem for Type1 Diabetes Mellitus (T1DM) patients is considered as anexample to highlight its main properties.