An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error
Abstract
In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for the class of functions whose gradient is bounded within a sector. Also, we show that the corresponding Lur\'e-type nonlinear system involves a double integrator, which demonstrates its ability to track a linearly varying optimal point with zero steady-state error. The algorithm is applied to solving a time-of-arrival based localization problem with constant velocity and the results show that the algorithm is able to estimate the source location with zero steady-state error.
Cite
@article{arxiv.2411.01826,
title = {An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error},
author = {Alex Xinting Wu and Ian R. Petersen and Valery Ugrinovskii and Iman Shames},
journal= {arXiv preprint arXiv:2411.01826},
year = {2024}
}
Comments
8 pages, 7 figures, submitted to 2025 American Control Conference