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In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
Many techniques originally developed in the context of deterministic control theory have been recently applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
This paper analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
We develop a mathematical model for sailboat navigation that can play the same role that the Black and Scholes model plays in mathematical finance: it captures essential features of sailboat navigation, it can provide insights that might…
This study focuses on optimizing species release $S_2$ to control species population $S_1$ through impulsive release strategies. We investigate the conditions required to remove species $S_1$, which is equivalent to the establishment of…
This paper investigates the solvability and optimal control of a class of impulsive stochastic differential equations (SDEs) within a Hilbert space setting. First, we establish the existence and uniqueness of mild solutions for the proposed…
We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different…
We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and…
In this paper, we consider joint drift rate control and impulse control for a stochastic inventory system under long-run average cost criterion. Assuming the inventory level must be nonnegative, we prove that a…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…