Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

TL;DR

This paper surveys recent advances in online feedback optimization for quadratic programs, introduces new convergence results for primal-dual algorithms with heterogeneous step sizes, and demonstrates applications in power system control.

Contribution

It provides novel convergence analysis for primal-dual online algorithms with heterogeneous gradient step sizes and illustrates their application in power system optimal control.

Findings

Convergence results for algorithms with heterogeneous step sizes

Application to adaptive and model-free online algorithms

Enhanced understanding of feedback optimization in power systems

Abstract

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems.