Related papers: Risk-Aware Stability of Discrete-Time Systems
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space"…
Accurate estimation of long-term risk is essential for the design and analysis of stochastic dynamical systems. Existing risk quantification methods typically rely on extensive datasets involving risk events observed over extended time…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
In this paper the linear and stationary Discrete-time systems with state variables and dynamic coefficients represented by fuzzy numbers are studied, providing some stability criteria, and characterizing the bounds of the set of solutions…