Related papers: Optimal Carbon Emission Control With Allowances Pu…
A new approach to feedback control design based on optimal control is proposed. Instead of expensive computations of the value function for different penalties on the states and inputs, we use a control Lyapunov function that amounts to be…
We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, the problem is constructed as a stochastic game with two players: the decision-maker (DM) chooses the `best' harvesting…
In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…
Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they…
This paper studies an optimal stochastic impulse control problem in a finite horizon with a decision lag, by which we mean that after an impulse is made, a fixed number units of time has to be elapsed before the next impulse is allowed to…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
There is much disagreement concerning how best to control global carbon emissions. We explore quantitatively how different control schemes affect the collective emission dynamics of a population of emitting entities. We uncover a complex…
This paper investigates the optimal control problems for the finite-horizon continuous-time Markov decision processes with delay-dependent control policies. We develop compactification methods in decision processes, and show that the…
As global climate change and environmental issues escalate, carbon reduction has emerged as a paramount global concern. Agriculture accounts for approximately 30% of global greenhouse gas emissions, making carbon reduction in this sector…
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…
The Bellman equation and its continuous-time counterpart, the Hamilton-Jacobi-Bellman (HJB) equation, serve as necessary conditions for optimality in reinforcement learning and optimal control. While the value function is known to be the…
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
We study the problem of optimal control of dissipative quantum dynamics. Although under most circumstances dissipation leads to an increase in entropy (or a decrease in purity) of the system, there is an important class of problems 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 study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
Stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than the the ones when the delay appears only in the state. This is particularly true when we look at the…
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and…