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We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction.…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
We investigate the emergence of non-linear diffusivity in kinetically constrained, one-dimensional symmetric exclusion processes satisfying the gradient condition. Recent developments introduced new gradient dynamics based on the Bernstein…
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential equations with regularly varying nonlinearity close to…
In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous- and discrete-time cases. The sufficient conditions for the existence and uniqueness of a…
The principal aim of the present work is to explore limit theorems for small random perturbations of dynamical systems with periodic impulse effects, in the limit of vanishing noise intensity. We start with a system whose time evolution is…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
We establish new conditions for obtaining uniform bounds on the moments of discrete-time stochastic processes. Our results require a weak negative drift criterion along with a state-dependent restriction on the sizes of the one-step jumps…