Data-driven Optimal Pole Placement via Sylvester Equations

Abstract

This paper proposes a data-driven framework for optimal pole placement, in which the objective function is defined as a weighted sum of a robustness measure of pole placement and the Frobenius norm of the feedback gain. To derive the optimization algorithm, we propose data-driven methods for solving Sylvester equations, where data-based expressions of Sylvester equations are introduced. By utilizing this result, a gradient-based optimization algorithm is presented. The effectiveness of the proposed algorithm is demonstrated through a numerical example.