TR2020-001

Finite-Time Convergence of Continuous-Time Optimization Algorithms via Differential Inclusions


    •  Romero, O., Benosman, M., "Finite-Time Convergence of Continuous-Time Optimization Algorithms via Differential Inclusions", Advances in Neural Information Processing Systems (NeurIPS) - Workshop, January 2020.
      BibTeX TR2020-001 PDF
      • @inproceedings{Romero2020jan,
      • author = {Romero, Orlando and Benosman, Mouhacine},
      • title = {Finite-Time Convergence of Continuous-Time Optimization Algorithms via Differential Inclusions},
      • booktitle = {Advances in Neural Information Processing Systems (NeurIPS) - Workshop},
      • year = 2020,
      • month = jan,
      • url = {https://www.merl.com/publications/TR2020-001}
      • }
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  • Research Areas:

    Control, Dynamical Systems

In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time stability and thus finite-time convergence with a provable bound on the settling time. In particular, for exact solutions to the aforementioned differential inequality, the settling-time bound is also exact, thus achieving prescribed finite-time convergence. We thus construct a class of discontinuous dynamical systems, of second order with respect to the cost function, that serve as continuous-time optimization algorithms with finite-time convergence and prescribed convergence time. Finally, we illustrate our results on the Rosenbrock function.