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Título del libro: European Control Conference (piscataway, N.J. Online), Ecc
Título del capítulo: A Finite-Time Convergent Primal-Dual Gradient Dynamics Based on the Multivariable Super-Twisting Algorithm

Autores UNAM:
OSCAR TEXIS LOAIZA; JOSE ANGEL MERCADO URIBE; JAIME ALBERTO MORENO PEREZ;
Autores externos:

Idioma:

Año de publicación:
2025
Palabras clave:

Dynamic algorithm; Finite-time; Finite-time convergence; Gradient dynamics; Homogeneity properties; Linear equality constraints; Multi variables; Optimization problems; Primal-dual; Super twisting algorithm


Resumen:

© 2025 EUCA.We propose a novel primal-dual gradient dynamics (PDGD) algorithm to dynamically solve an optimization problem with linear equality constraints in finite time. To ensure finite-time convergence, we endow the PDGD with suitable homogeneity properties. More precisely, departing from the standard PDGD and based on the associated Lagrangian of the optimization problem, the algorithm is derived by suitably combining a change of coordinates of the standard PDGD with the multivariable super-twisting algorithm. In our new coordinates, the proposed PDGD's global convergence to the optimal solution of the optimization problem is then proven via a smooth, strong Lyapunov function. Additionally, we provide a numerical example to compare the performance of our algorithm with existing approaches from the literature.


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