TR2020-085

Continuous-Time Optimization of Time-Varying Cost Functions via Finite-Time Stability with Pre-Defined Convergence Time


    •  Romero, O., Benosman, M., "Continuous-Time Optimization of Time-Varying Cost Functions via Finite-Time Stability with Pre-Defined Convergence Time", American Control Conference (ACC), June 2020.
      BibTeX TR2020-085 PDF
      • @inproceedings{Romero2020jun,
      • author = {Romero, Orlando and Benosman, Mouhacine},
      • title = {Continuous-Time Optimization of Time-Varying Cost Functions via Finite-Time Stability with Pre-Defined Convergence Time},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2020-085}
      • }
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  • Research Area:

    Optimization

In this paper, we propose a new family of continuous-time optimization algorithms for time-varying, locally strongly convex cost functions, based on discontinuous second-order gradient optimization flows with provable finite-time convergence to local optima. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of arbitrary time-varying differential inclusions, particularly of the Filippov type. We then prove the convergence of our proposed flows in finite time. We illustrate the performance of our proposed flows on a quadratic cost function to track a decaying sinusoid.

 

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