Related papers: Hamilton-Jacobi equations for optimal control on m…
This article is devoted to the study of lower semicontinuous solutions of Hamilton-Jacobi equations with convex Hamiltonians in a gradient variable. Such Hamiltonians appear in the optimal control theory. We present a necessary and…
This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the…
In the paper, we consider a path-dependent Hamilton-Jacobi equation with coinvariant derivatives over the space of continuous functions. Such equations arise from optimal control problems and differential games for time-delay systems. We…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
We establish the existence and uniqueness of viscosity solutions within a domain $\Omega\subseteq\mathbb R^n$ for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific…
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
Stochastic optimal control control problems with merely measurable coefficients are not well understood. In this manuscript, we consider fully non-linear stochastic optimal control problems in infinite horizon with measurable coefficients…
In this paper we study a first extension of the theory of mild solutions for HJB equations in Hilbert spaces to the case when the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
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…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…