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We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion.…
Controllers for autonomous systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modelled as process noise, and common assumptions are that the underlying distributions are…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…
We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow…
In this paper, we study the effect of small Brownian noise on a switching dynamical system which models a first-order DC/DC buck converter. The state vector of this system comprises a continuous component whose dynamics switch, based on the…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We design the controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a…
We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but non-causal, asymptotic…
In this paper, we establish a small time large deviation principle (small time asymptotics) for the dynamical $\Phi^4_1$ model, which not only involves study of the space-time white noise with intensity $\sqrt{\varepsilon}$, but also the…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently…
Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements. This work investigates the robustness of the Loewner approach to noise. The key finding is that…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…