Data-Driven Synthesis of Optimization-Based Controllers for Regulation of Unknown Linear Systems

Abstract

The exact pole placement problem concerns computing a feedback gain that will assign the poles of a system, controlled via static state feedback, 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 gains 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 objectives, such as feedback stabilization or meeting transient performance specifications, can be achieved without first identifying a system model. Numerical experiments demonstrate the benefits of the data-driven pole-placement approach as compared to its model-based counterpart.

Hierarchical Coordinated Fast Frequency Control using Inverter-Based Resources

“…Our tuning recommendation is L = G(1) † , where G(1) = C(zI n − A) −1 B d | z=1 is the DC gain of the system (2) from input d to output y. This selection will be justified in our theory to follow, and the matrix G(1) can be obtained directly from the same historical data used to construct P in (7); see [34,Thm. 4.1] for details on that construction.…”