Related papers: Metastability of random maps: a resolvent approach

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp…

An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…

We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…

This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

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…

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…

We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…

The Markovian dynamics of a qubit is investigated in the scheme of random unitary dynamics, where Kraus operators are changed by an extra noise. The behavior of Markovianity is explored in the perturbed scenario. We provide a new algorithm…

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…

This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…

This paper proposes a Lyapunov approach to the design of a multivariable generalized Super-Twisting algorithm (MGSTA), which is able to control a system with perturbations and uncertain control matrix, both depending on time and the system…

This paper addresses the challenge of a particular class of noisy state observations in Markov Decision Processes (MDPs), a common issue in various real-world applications. We focus on modeling this uncertainty through a confusion matrix…