Related papers: Stochastic Optimal Control with Delay in the Contr…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation.…
We study the optimal control of an infinite-dimensional stochastic system governed by an SDE in a separable Hilbert space driven by cylindrical stable noise. We establish the existence and uniqueness of a mild solution to the associated HJB…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…
We study the problem of generating control laws for systems with unknown dynamics. Our approach is to represent the controller and the value function with neural networks, and to train them using loss functions adapted from the…
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a…
This paper studies the optimal control problems of stochastic evolution equations with infinite delay of general functional type. By introducing a non-anticipative path derivative and its infinite-window dual operator, we derive the…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman…
This paper deals with junction conditions for Hamilton-Jacobi-Bellman (HJB) equations for finite horizon control problems on multi-domains. We consider two different cases where the final cost is continuous or lower semi-continuous. In the…
Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…
Designing optimal controllers for nonlinear dynamical systems often relies on reinforcement learning and adaptive dynamic programming (ADP) to approximate solutions of the Hamilton Jacobi Bellman (HJB) equation. However, these methods…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit…
In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…
Optimal feedback controllers for nonlinear systems can be derived by solving the Hamilton-Jacobi-Bellman (HJB) equation. However, because the HJB is a nonlinear partial differential equation, numerical methods typically provide only…