Fixed-Time Gradient Dynamics With Time-Varying Coefficients for Continuous-Time Optimization

In this article, we propose 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 continuo...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 68; no. 7; pp. 4383 - 4390
Main Authors Nguyen, Lien T., Yu, Xinghuo, Eberhard, Andrew, Li, Chaojie
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Asymptotic stability
Coefficients
Continuous-time optimization
Convergence
Dynamic stability
Dynamical systems
Dynamics
fixed-time convergence
gradient-based method
Lyapunov function
Lyapunov methods
Newton-like method
Numerical stability
Optimization
stability
Stability criteria
time-varying systems
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Summary:In this article, we propose 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 optimization 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3206251