Related papers: Hamilton-Jacobi equations for optimal control on m…

We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…

We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the…

We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered…

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…

We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf…

This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…

The Hamilton-Jacobi equation on metric spaces has been studied by several authors; following the approach of Gangbo and Swiech, we show that the final value problem for the Hamilton-Jacobi equation has a unique solution even if we add a…

This article is devoted to the optimal control of state equations with memory of the form: ?[x(t) = F(x(t),u(t), \int_0^{+\infty} A(s) x(t-s) ds), t>0, with initial conditions x(0)=x, x(-s)=z(s), s>0.]Denoting by $y_{x,z,u}$ the solution of…

Given a coercive Hamiltonian which is quasi-convex with respect to the gradient variable and periodic with respect to time and space at least "far away from the origin", we consider the solution of the Cauchy problem of the corresponding…

This paper deals with the optimal control of systems governed by nonlinear systems of conservation laws at junctions. The applications considered range from gas compressors in pipelines to open channels management. The existence of an…

We discuss a class of time-dependent Hamilton-Jacobi equations, where an unknown function of time is intended to keep the maximum of the solution to the constant value 0. Our main result is that the full problem has a unique viscosity…

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…

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…

Maximum entropy reinforcement learning (RL) methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, most of existing techniques are designed for discrete-time systems. As a…

We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the…

This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…

Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…

We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo's classical viability theorems (necessary and sufficient conditions for mean viability). As an application, we…

Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…

A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved. Key words: Cahn-Hilliard…