Online Data-driven Stabilization of Switched Linear Systems

We consider the stabilization problem of a discrete-time system that switches among a finite set of unknown linear subsystems under unknown switching signal. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the proposed online implementation is therefore the ability of the controller to automatically adjust to changes in the operating mode of the system. We show that the proposed control mechanism guarantees exponential stability of the closed-loop switched system under sufficiently slow switching. The effectiveness of the approach is illustrated via a numerical example.