相关论文: An initial condition reconstruction in Hamilton-Ja…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
We consider a semilinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity which is related to a stochastic control problem with fuel constraint. The fuel constraint translates into a singular initial condition…
The Hamilton-Jacobi equation in the sense of Poincar\'e, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our…
We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the so-called locally optimal solution to time-optimal control…
We consider the class of control systems where the differential equation, state and control system are described by polynomials. Given a set of trajectories and a class of Lagrangians, we are interested to find a Lagrangian in this class…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…
We consider a Cauchy problem for a (first-order) path-dependent Hamilton--Jacobi equation with coinvariant derivatives and a right-end boundary condition. Such problems arise naturally in the study of properties of the value functional in…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
This paper introduces a notion of viscosity solutions for second order elliptic Hamilton-Jacobi-Bellman (HJB) equations with infinite delay associated with infinite-horizon optimal control problems for stochastic differential equations with…
We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…
We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians. We consider the Neumann or oblique boundary condition, the state constraint boundary…
We study the Cauchy problem for the Hamilton-Jacobi equation with a semiconcave initial condition. We prove an inequality between two types of weak solutions emanating from such an initial condition (the variational and the viscosity…
In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super…
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the…
We study semi Lagrangian approximation schemes for Hamilton Jacobi Bellman equations arising from finite horizon optimal control problems. Classical error estimates for these schemes include the term $\frac{1}{\Delta t}$ which leads to…
An optimal control problem described by the Hamilton-Jacobi-Bellman equation can be developed into a problem that can be solved by general computational fluid dynamics packages. We describe how this formulation would allow a classical…