Related papers: Leveraging Stochasticity for Open Loop and Model P…
In plasma turbulence theory, due to the complexity of the system with many non-linearly interacting waves, the dynamics of the phases is often disregarded and the so-called random-phase approximation (RPA) is used assuming the existence of…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…
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…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky…
We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the…
By extending \cite{bensoussan2015control}, we implement the proposal of Lions \cite{lions14} on studying mean field games and their master equations via certain control problems on the Hilbert space of square integrable random variables. In…
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…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
Experimental data from an experiment on drift--waves in plasma is presented. The experiment provides a space--time diagnostic and has a control parameter that permits the study of the transition from a stable plasma to a turbulent plasma.…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…