6 papers · 1 filter
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…
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…
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…
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…
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…