We study averaging-learning dynamics without an exogenous ground truth: the reference signal is generated endogenously by the population. The dynamics combine a time-varying averaging matrix, a learning-source matrix, and a learning matrix, typically diagonal. Dobrushin-type contraction controls the decay of oscillations and yields asymptotic agreement. Under a summability condition, the backward products converge exponentially to rank-one limits. With summable perturbations, the process converges to a random consensus state. For i.i.d. perturbations, we prove a central limit theorem for the centered process: the limiting Gaussian law is supported on the agreement direction. Thus, despite the multi-agent dynamics, the long-time fluctuations are asymptotically one-dimensional. We also record a pairwise Dobrushin formulation that clarifies the dynamic agreement-class geometry underlying the one-class regime.
A time-varying quadratic norm is constructed that turns this window contraction into an exact one-step Lyapunov identity, leading to coupled one-step recursions for the centroid and disagreement errors, without unrolling the dynamics over communication windows.
Many real-world processes exhibit long-range dependence, where the current state depends on a slowly decaying trace of past states rather than on the most recent state alone. This paper studies system identification for discrete-time fractional-order linear time-invariant systems from a single observed trajectory of le...
Xiao-Le Zhang, Zi-Yi Zhang, Ze-Hao Zhao et al.· 0 citations
This work shows that the corresponding linearized dynamics leads naturally to a semigroup formulation, and proves norm-bounds on the corresponding semigroup perturbations, in the form of explicit finite-time perturbation estimates.
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon et al.· 0 citations
This work provides a system-theoretic interpretation of generalization in learning-enabled dynamical systems arising in data-driven optimization and feedback control approximation, and establishes a matrix inequality-based certificate and a uniform stability bound that separates the one-sample sensitivity of the learne...
A prelimit coupling framework for analyzing nonsmooth stochastic approximation procedures is developed, which establishes Wasserstein convergence to a unique stationary distribution, characterize the limiting steady-state distribution as the step size vanishes, and shows that nonsmoothness can create a bias of order of...
A Brownian-bridge self-normalizer yields asymptotically pivotal confidence regions for prespecified state-value contrasts for prespecified state-value contrasts without estimating the long-run covariance or selecting a bandwidth or batch length.
