Related papers: Stochastic Contraction in Riemannian Metrics
The stability and the basin of attraction of a periodic orbit can be determined using a contraction metric, i.e., a Riemannian metric with respect to which adjacent solutions contract. A contraction metric does not require knowledge of the…
This paper studies fixed step-size stochastic approximation (SA) schemes, including stochastic gradient schemes, in a Riemannian framework. It is motivated by several applications, where geodesics can be computed explicitly, and their use…
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…
The stochastic dynamics of orthogonal metal cutting with both regenerative and nonsmooth frictional effects are investigated numerically in this paper. The shortcomings of neglecting nonsmoothness in frictional and stochastic effects in…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
In the presence of sample selection, Lee's (2009) nonparametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, whose empirical validity is sometimes unclear.…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in SST is…
Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…