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Achieving precise control of colloidal self-assembly into specific patterns remains a longstanding challenge due to the complex process dynamics. Recently, machine learning-based state representation and reinforcement learning-based control…
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to…
In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin…
In this paper we consider the controllability of certain class of non-autonomous neutral evolution stochastic functional differential equations, with time varying delays, driven by a fractional Brownian motion in a separable real Hilbert…
This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…
Control of stochastic systems is a challenging open problem in statistical physics, with potential applications in a wealth of systems from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely…
We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
The main purpose of this paper is to discuss detailed the stochastic LQ control problem with random coefficients where the linear system is a multidimensional stochastic differential equation driven by a multidimensional Brownian motion and…
We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be…
Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a…
We consider a d-dimensional stochastic differential equation with additive noise and a drift coefficient which is assumed only to be a bounded Borel function. We show that, for almost all choices of the driving Brownian path, the equation…
This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target…
In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a…