4 papers · 1 filter
Universal Formulas for Safe Control and Their Neural Network Approximations
Pol Mestres, Jorge Cortés, Eduardo D. Sontag
We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the fact that a var…
On the (almost) Global Exponential Convergence of the Overparameterized Policy Optimization for the LQR Problem
Moh Kamalul Wafi, Arthur Castello B. de Oliveira, Eduardo D. Sontag
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of t…
Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag +1
This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonli…
Remarks on the Polyak-Lojasiewicz inequality and the convergence of gradient systems
Arthur Castello B. de Oliveira, Leilei Cui, Eduardo D. Sontag
This work explores generalizations of the Polyak-Lojasiewicz inequality (PLI) and their implications for the convergence behavior of gradient flows in optimization problems. Motiva…