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We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the…
This contribution reviews critically the existing entropy measures for probabilistic hesitant fuzzy sets (PHFSs), and demonstrates that these entropy measures fail to effectively distinguish a variety of different PHFSs in some cases. In…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
Dynamical Systems is a field that studies the collective behavior of objects that update their states according to some rules. Discrete-time Boolean Finite Dynamical System (DT-BFDS) is a subfield where the systems have some finite number…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…