Fixed-Time Convergence in Continuous-Time Optimization: A Fractional Approach

Continuous-time optimization is now an active research field and many valuable results have been proposed. As is known, a fast convergence speed is always desirable for an optimization algorithm and thus the fixed-time convergence in continuous-time optimization is considered in this letter. Differe...

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Veröffentlicht in:IEEE control systems letters Jg. 7; S. 631 - 636
Hauptverfasser: Chen, Yuquan, Wang, Fumian, Wang, Bing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: IEEE 2023
Schlagworte:
Control systems
Convergence
fixed-time convergence
Gradient method
Laplace equations
Mittag-Leffler function
non-singular
Optimization
second-order algorithm
Shape
Tuning
Upper bound
ISSN:2475-1456, 2475-1456
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Zusammenfassung:Continuous-time optimization is now an active research field and many valuable results have been proposed. As is known, a fast convergence speed is always desirable for an optimization algorithm and thus the fixed-time convergence in continuous-time optimization is considered in this letter. Different from existing fixed-time schemes, a novel fixed-time gradient method with a fractional adaptive gain is proposed, whose convergence time is determined by the first positive zero of a Mittag-Leffler function and independent of initial conditions. Furthermore, to avoid the possible singularity, two non-singular fixed-time gradient methods are proposed. Finally, all the results are extended to the second-order algorithm, whose convergence time is proven to be independent of both initial conditions and the shape of the target function.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2022.3213745