@misc{TexisLoaizaMercadoUribeMorenoetal., author = {Texis-Loaiza, Oscar and Mercado-Uribe, Angel and Moreno, Jaime A. and Schiffer, Johannes}, title = {A finite-time convergent primal-dual gradient dynamics based on the multivariable super-twisting algorithm}, series = {2025 European Control Conference (ECC)}, journal = {2025 European Control Conference (ECC)}, publisher = {IEEE}, address = {New York, NY}, isbn = {978-3-907144-12-1}, doi = {10.23919/ECC65951.2025.11186834}, pages = {1892 -- 1898}, abstract = {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.}, language = {en} } @misc{TexisLoaizaMorenoMercadoUribeetal., author = {Texis-Loaiza, Oscar and Moreno, Jaime A. and Mercado-Uribe, Angel and Schiffer, Johannes}, title = {A third-order bl-homogeneous sliding mode observer for uncertain triangular nonlinear systems}, series = {2025 European Control Conference (ECC)}, journal = {2025 European Control Conference (ECC)}, publisher = {IEEE}, address = {New York, NY}, isbn = {978-3-907144-12-1}, doi = {10.23919/ECC65951.2025.11186860}, pages = {1955 -- 1960}, abstract = {In this paper, we propose a global third-order homogeneous in the bi-limit sliding mode observer (BL-H SMO) that can estimate the states of an uncertain nonlinear system with unknown inputs in finite time. The system must be strongly observable w.r.t. unknown inputs (UIs) and uniformly observable w.r.t. known inputs. To handle the UIs and non-Lipschitz nonlinearities, the proposed observer combines sliding-mode and high-gain observers, extending the generalized super-twisting observer. The convergence of the BL-H SMO to the system states is proven through a Lyapunov function. Finally, to showcase the effectiveness of the proposed method, the paper includes an academic example and a practical example, namely a three-phase converter with LCL-filter.}, language = {en} }