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Time-varying continuous-time optimisation with pre-defined finite-time stability.
- Source :
-
International Journal of Control . Dec 2021, Vol. 94 Issue 12, p3237-3254. 18p. - Publication Year :
- 2021
-
Abstract
- In this paper, we propose a new family of continuous-time optimisation algorithms based on discontinuous second-order gradient optimisation flows, with finite-time convergence guarantees to local optima, for locally strongly convex (time-varying) cost functions. To analyse our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of (time-varying) differential inclusions. We then prove the convergence of these second-order flows in finite-time. In some particular cases, we can show that the finite-time convergence can be pre-defined by the user. We propose a robustification of the flows to bounded additive uncertainties and extend some of the results to the case of constrained optimisation. We show the performance of these flows on well-known optimisation benchmarks, namely, the Rosenbrock function, and the Rastringin function. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00207179
- Volume :
- 94
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- International Journal of Control
- Publication Type :
- Academic Journal
- Accession number :
- 153407859
- Full Text :
- https://doi.org/10.1080/00207179.2020.1756415