Related papers: Numerical Solution of the Dynamic Programming Equa…
We study the approximation of parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the…
This paper presents a two-stage framework for constrained near-optimal feedback control of input-affine nonlinear systems. An approximate value function for the unconstrained control problem is computed offline by solving the…
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…
The paper deals with a Bolza optimal control problem for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal…
We study a family of stationary Hamilton-Jacobi-Bellman (HJB) equations in Hilbert spaces arising from stochastic optimal control problems. The main difficulties to treat such problems are: the lack of smoothing properties of the linear…
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…
This paper derives the Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems for cost functions with fractional discount rate from the Bellman's principle of optimality. The fractional discount rate is described by…
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…
This work concerns the optimal control problem for McKean-Vlasov SDEs. In order to characterize the value function, we develop the viscosity solution theory for Hamilton-Jacobi-Bellman (HJB) equations on the Wasserstein space using…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
Devising optimal interventions for diffusive systems often requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, a nonlinear backward partial differential equation (PDE), that is, in general, nontrivial to solve. Existing…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…
In this article, we study optimal feedback control synthesis of stochastic 2D Navier-Stokes equations perturbed Levy type noise with distributed stochastic control process acting on the state equation. We use the dynamic programming…
The present paper addresses the issue of choosing an optimal dynamic reinsurance policy, which is state-dependent, for an insurance company that operates under multiple insurance business lines. The optimal survival function is…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
An optimal control problem is considered for a stochastic differential equation with the cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). This kind of cost functional can cover the general…