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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| Veröffentlicht in: | IEEE transactions on automatic control 2023-07, Vol.68 (7), p.4383-4390 |
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| container_title | IEEE transactions on automatic control |
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| creator | Nguyen, Lien T. Yu, Xinghuo Eberhard, Andrew Li, Chaojie |
| description | 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. |
| doi_str_mv | 10.1109/TAC.2022.3206251 |
| format | Article |
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Simulation results are given to show the effectiveness of the proposed fixed-time gradient dynamics with tunable time-varying coefficients for continuous-time optimization.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2022.3206251</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>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</subject><ispartof>IEEE transactions on automatic control, 2023-07, Vol.68 (7), p.4383-4390</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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Simulation results are given to show the effectiveness of the proposed fixed-time gradient dynamics with tunable time-varying coefficients for continuous-time optimization.</description><subject>Asymptotic stability</subject><subject>Coefficients</subject><subject>Continuous-time optimization</subject><subject>Convergence</subject><subject>Dynamic stability</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>fixed-time convergence</subject><subject>gradient-based method</subject><subject>Lyapunov function</subject><subject>Lyapunov methods</subject><subject>Newton-like method</subject><subject>Numerical stability</subject><subject>Optimization</subject><subject>stability</subject><subject>Stability criteria</subject><subject>time-varying systems</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><recordid>eNo9kN9LwzAQgIMoOKfvgi8FnzsvSdMmj6O6KQz2MvVFCGl-aIZtZ9OC8683peLTcXff3XEfQtcYFhiDuNstywUBQhaUQE4YPkEzzBhPCSP0FM0AME8F4fk5ughhH9M8y_AMva38tzXpztc2WXfKeNv0yf2xUbXXIXn1_Ucy9tIX1R19856UrXXO6xELiWu7WGh63wztEKYl20Pva_-jet82l-jMqc9gr_7iHD2vHnblY7rZrp_K5SbVlNI-pUYAGF4I0A6ynGBlmWBMMQvUGkeoIYa4ShSVNjbTeQVau0iB4oryqqBzdDvtPXTt12BDL_ft0DXxpCScQoaL6CRSMFG6a0PorJOHztfxL4lBjg5ldChHh_LPYRy5mUa8tfYfF5wLgnP6C1lmbdM</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Nguyen, Lien T.</creator><creator>Yu, Xinghuo</creator><creator>Eberhard, Andrew</creator><creator>Li, Chaojie</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| source | IEEE Electronic Library (IEL) |
| 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 |
| title | Fixed-Time Gradient Dynamics With Time-Varying Coefficients for Continuous-Time Optimization |
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