Related papers: Hamilton-Jacobi equations for optimal control on m…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
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…
The paper concerns the infinite dimensional Hamilton-Jacobi-Bellman equation related to optimal control problem regulated by a transport equation with boundary control. A suitable viscosity solution approach is needed in view of the…
We consider an optimal control on networks in the spirit of the works of Achdou et al. (2013) and Imbert et al. (2013). The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible…
This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…
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 aim of this work is to deal with a discontinuous Hamilton-Jacobi equation in the whole euclidian N-dimensional space, associated to a possibly unbounded optimal control problem. Here, the discontinuities are located on a hyperplane and…
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 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…
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 investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is…
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…
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 paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB)…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value…
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…
In this article, a class of optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential equations with delays. This type…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by…