Related papers: Singular Control of (Reflected) Brownian Motion: A…
In this paper we study weak solutions for the following type of stochastic differential equation \[ dX_{t}=dW_{t}+b(t, X_{t})dt, \quad t\ge s, \quad X_{s}=x, \] where $b: [0,\infty) \times \mathbb{R}^{d} \to \mathbb{R}^{d}$ is a measurable…
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140,…
The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests…
The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…
An asymptotic framework for optimal control of multiclass stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP) and their equivalent workload…
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
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…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by Partial Differential Equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled "open loop-closed loop" fashion that is…
This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a…
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control…
This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region…
The multiple disorder problem seeks to determine a sequence of stopping times which are as close as possible to the unknown times of disorders at which the observation process changes its probability characteristics. We derive closed form…
In this study, we conduct experimental investigations on the behavior of confined self-propelled particles within a circular arena, employing small commercial robots capable of locomotion, communication, and information processing. These…