Fixed-Time Gradient Dynamics With Time-Varying Coefficients for Continuous-Time Optimization
Lien T. Nguyen, Xinghuo Yu, Andrew Eberhard, Chaojie Li
Abstract
In this paper, we propose a fixed-time gradient dynamics with time-varying coefficients for continuous-time optimization. We first investigate the Lyapunov stability conditions that allow us to achieve fixed-time stability of the time-varying dynamical systems. We then use them to deal with continuous-time optimisation problems. We show that under the proposed fixed-time gradient dynamics and by choosing time-varying coefficients, the searching trajectories converge to their optima in fixed-time from any initial points with a very fast rate. Simulation results are given to show the effectiveness of the proposed fixed-time gradient dynamics with tunable time-varying coefficients for continuous-time optimization.