A Feedback-Based Optimization Algorithm with Designed Gain Matrix

In this paper, we propose a gradient projection algorithm aimed at improving the transient performance of feedback-based optimization (FO) for linear dynamical systems. Our approach leverages a specifically designed gain matrix, replacing the usual scalar step size to enhance trajectory efficiency and reduce oscillations. By solving a semi-definite programming, we select the gain matrix to trade off between convergence rate and oscillation minimization. Compared to the standard FO algorithms, our method demonstrates improved transient performance in numerical simulations and in turn faster convergence.