Data-Driven Exact Pole Placement for Linear Systems

The exact pole placement problem concerns computing a static feedback law for a linear dynamical system that will assign its poles at a set of pre-specified locations. This is a classic problem in feedback control and numerous methodologies have been proposed in the literature for cases where a model of the system to control is available. In this paper, we study the problem of computing feedback laws for pole placement (and, more generally, eigenstructure assignment) directly from experimental data. Interestingly, we show that the closed-loop poles can be placed exactly at arbitrary locations without relying on any model description but by using only finite-length trajectories generated by the open-loop system. In turn, these findings imply that classical control goals, such as feedback stabilization or meeting transient transient performance specifications, can be achieved directly from data without first identifying a system model. Numerical experiments demonstrate the benefits of the data-driven pole-placement approach compared to its model-based counterpart.