Related papers: Optimal Control for a Nonlinear Stochastic Parabol…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
In this paper we study optimal advertising problems that models the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we…
This paper is concerned with the partial information optimal control problem of wa controlled forward-backward stochastic differential equation of jump diffusion with correlated noises between the system and the observation. For this type…
Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…
We consider the problem of nonlinear stochastic optimal control. This problem is thought to be fundamentally intractable owing to Bellman's "curse of dimensionality". We present a result that shows that repeatedly solving an open-loop…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…
In this paper, we study the existence of an optimal strategy for the stochastic control of diffusion in general case and a saddle-point for zero-sum stochastic differential games. The problem is formulated as an extended BSDE with…
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
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 study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…
This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff…
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…