11 papers
Smooth globally PLI functions are nonlinear least-squares, and so are their gradient-dominated cousins
Eduardo D. Sontag
Boumal, Criscitiello and Rebjock (BCR) proved that if is a contractible, connected and complete Riemannian manifold, then every smooth function satisfying the…
On input-output persistency and the interconnection of positive nonlinear systems
Arthut Castello B. de Oliveira, Moh K. Wafi, Eduardo D. Sontag
In this paper we study feedback interconnections of positive nonlinear SISO systems and introduce two complementary properties: persistent-input/persistent-output (PIPO) for the pl…
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…
Autoencoding Dynamics: Topological Limitations and Capabilities
Matthew D. Kvalheim, Eduardo D. Sontag
Given a "data manifold" and "latent space" , an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\t…
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…
Small-Covariance Noise-to-State Stability of Stochastic Systems and Its Applications to Stochastic Gradient Dynamics
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag
This paper studies gradient dynamics subject to additive random noise, which may arise from sources such as stochastic gradient estimation, measurement noise, or stochastic samplin…