Related papers: Capacities, Measurable Selection and Dynamic Progr…

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate…

Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…

We study stochastic motion planning problems which involve a controlled process, with possibly discontinuous sample paths, visiting certain subsets of the state-space while avoiding others in a sequential fashion. For this purpose, we first…

This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…

We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…

We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be…

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…

We construct an abstract framework in which the dynamic programming principle (DPP) can be readily proven. It encompasses a broad range of common stochastic control problems in the weak formulation, and deals with problems in the…

In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…

Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…

In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…

We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…

The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…

Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Combinatorial optimisation is the practice of selecting the best constituent…

Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…

We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…