Modeling and Control of Switched Systems, with Application to Biomedical Problems

Switched systems have attracted considerable attention in both theoretical research and practical applications, as they provide an effective framework for modelling and controlling real-world dynamical systems with complex behaviour. These systems are typically represented by a finite collection of dynamics (possibly controlled), together with a switching signal that designates, at each time, which subsystem is active [1]. The analysis of such systems is far from trivial, and significant efforts have been made to characterise their properties [2] and to establish conditions for controllability and stabilizability [3,4]. Furthermore, SS are subject not only to state and input constraints but also to minimum and maximum activation times for each subsystem, which makes invariance and stability analysis particularly challenging [5-7].

The design of control strategies - especially optimisation-based approaches such as model predictive control (MPC) - that exploit the structure of switched systems is also an area of growing interest [6-8]. Biomedical applications (ranging from cancer treatment [8] to type 1 diabetes [10], and particularly antimicrobial resistance [8,11]) make use of switched systems to model therapies involving the sequential combination of different drugs, with the aim of optimising treatment efficacy. In this context, constraints naturally arise due to pharmacological and clinical limitations on the frequency and duration of treatment changes, often dictated by efficacy thresholds and tolerances to toxicity [12,13]. Regarding antimicrobial resistance, preliminary switching strategies have already proven useful not only for improving treatment outcomes but also for preventing mutation escape [8,11].