Related papers: Asymptotic problems in optimal control with a vani…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
The paper is devoted to the asymptotic behavior of value functions of abstract control problem with the long-time and discounted averages. The Uniform Tauberian Theorem for these problems states that the uniform convergence of value…
We study an ergodic problem associated to a non-local Hamilton-Jacobi equation defined on the whole space $\lambda-\mathcal{L}[u](x)+|Du(x)|^m=f(x)$ and determine whether (unbounded) solutions exist or not. We prove that there is a…
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…
The stochastic linear--quadratic regulator problem subject to Gaussian disturbances is well known and usually addressed via a moment-based reformulation. Here, we leverage polynomial chaos expansions, which model random variables via series…
In this paper, infinite horizon stochastic difference equations and backward stochastic difference equations with fractional noises are studied. The main difficulty comes from fractional noises on infinite horizon. Motivated by…
We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which…
In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…
This paper is concerned with a time-inconsistent stochastic optimal control problem in an infinite time horizon with a non-degenerate diffusion in the state equation. A major assumption is that people become rational after a large time.…
IIn this paper we show that some HJB equations arising from both finite and infinite horizon stochastic optimal control problems have a regular singular point at the origin. This makes them amenable to solution by power series techniques.…
This work addresses the finite-horizon robust covariance control problem for discrete-time, partially observable, linear system affected by random zero mean noise and deterministic but unknown disturbances restricted to lie in what is…
We consider a problem of optimal control of an infinite horizon system governed by forward-backward stochastic differential equations with delay. Sufficient and necessary maximum principles for optimal control under partial information in…
This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive…
We consider a class of diffusions controlled through the drift and jump size, and driven by a jump L\'evy process and a nondegenerate Wiener process, and we study infinite horizon (ergodic) risk-sensitive control problem for this model. We…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
In this work the synthesis of approximate optimal and smooth feedback laws for infinite horizon optimal control problems is addressed. In this regards, $L^{p}$ type error bounds of the approximating smooth feedback laws are derived,…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed…
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in…
In this paper, we prove both necessary and sufficient maximum principles for infinite horizon discounted control problems of stochastic Volterra integral equations with finite delay and a convex control domain. The corresponding adjoint…