Optimal Trajectory Tracking Using Newton and Levenberg-Marquardt-Like Algorithms for Constrained Time-Varying Optimization

Abstract

In this paper, we propose continuous-time algorithms for tracking the optimal trajectory of time-varying optimization problems with time-varying constraints in a predefined time, where the time of convergence is selected a priori. A robust Newton-like approach is developed for the cases, where the exact knowledge of the rate of change of the gradient of objective function is unknown. Levenberg-Marquardt-like algorithm is proposed for the cases when the Hessian of the objective function is singular or near singular. Lyapunov-based convergence analysis is discussed for the proposed algorithms. Simulation results for time-varying optimization problems show the efficacy of the proposed approach. We demonstrate the applicability of the proposed method through its use in a collision-free robot navigation problem. © 2025 John Wiley & Sons Ltd.