28 citations · 32 across the 16 of their papers we have counts for
16 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…
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…
Some remarks on gradient dominance and LQR policy optimization
Eduardo D. Sontag
Solutions of optimization problems, including policy optimization in reinforcement learning, typically rely upon some variant of gradient descent. There has been much recent work i…
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…
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…
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…
Global linearization of asymptotically stable systems without hyperbolicity
Matthew D. Kvalheim, Eduardo D. Sontag
We give a proof of an extension of the Hartman-Grobman theorem to nonhyperbolic but asymptotically stable equilibria of vector fields. Moreover, the linearizing topological conjuga…
Convergence Analysis of Gradient Flow for Overparameterized LQR Formulations
Arthur Castello B. de Oliveira, Milad Siami, Eduardo D. Sontag
Motivated by the growing use of artificial intelligence (AI) tools in control design, this paper analyses the intersection between results from gradient methods for the model-free…
Regularizing Numerical Extremals Along Singular Arcs: A Lie-Theoretic Approach
Arthur Castello Branco de Oliveira, Milad Siami, Eduardo D. Sontag
Numerical ``direct'' approaches to time-optimal control often fail to find solutions that are singular in the sense of the Pontryagin Maximum Principle, performing better when sear…
Properties of Immersions for Systems with Multiple Limit Sets with Implications to Learning Koopman Embeddings
Zexiang Liu, Necmiye Ozay, Eduardo D. Sontag
Linear immersions (such as Koopman eigenfunctions) of a nonlinear system have wide applications in prediction and control. In this work, we study the properties of linear immersion…
Small-Disturbance Input-to-State Stability of Perturbed Gradient Flows: Applications to LQR Problem
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag
This paper studies the effect of perturbations on the gradient flow of a general nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation…
Why should autoencoders work?
Matthew D. Kvalheim, Eduardo D. Sontag
Deep neural network autoencoders are routinely used computationally for model reduction. They allow recognizing the intrinsic dimension of data that lie in a -dimensional subset…
Epigenetic factor competition reshapes the EMT landscape
M. Ali Al-Radhawi, Shubham Tripathi, Yun Zhang +2
The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene regulato…