An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error

TL;DR

This paper introduces an online optimization algorithm capable of tracking a linearly changing optimal point with zero steady-state error, applicable to nonconvex problems and demonstrated on localization tasks.

Contribution

The paper presents a novel online algorithm with proven convergence for nonconvex problems with linearly varying optima, including a stability analysis and practical application.

Findings

Algorithm guarantees global convergence under certain conditions.

Successfully applied to source localization with zero steady-state error.

Demonstrates effectiveness in tracking linearly varying optima.

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.