Related papers: Optimal control problems governed by two dimension…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on…
In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…
We formulate the the generalized Forchheimer equations for the three-dimensional fluid flows in rotating porous media. By implicitly solving the momentum in terms of the pressure's gradient, we derive a degenerate parabolic equation for 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…
This paper studies (single-time and multitime) optimal control problems on a nonholonomic manifold (described either by the kernel of a Gibbs-Pfaff form or by the span of appropriate vector fields). For both descriptions we analyse:…
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger…
We propose, study, and compute solutions to a class of optimal control problems for hyperbolic systems of conservation laws and their viscous regularization. We take barotropic compressible Navier--Stokes equations (BNS) as a canonical…
We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…
Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and…
This article is devoted to the optimal control of state equations with memory of the form: ?[x(t) = F(x(t),u(t), \int_0^{+\infty} A(s) x(t-s) ds), t>0, with initial conditions x(0)=x, x(-s)=z(s), s>0.]Denoting by $y_{x,z,u}$ the solution of…
This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland's variational principle, we obtain…
This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…
We study optimal control problems governed by abstract infinite dimensional stochastic differential equations using the dynamic programming approach. In the first part, we prove Lipschitz continuity, semiconcavity and semiconvexity of the…
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. The observation operator maps a solution of the Primitive Equations to…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
In this paper we study the optimality condition for the Venttsel boundary control of a parabolic equation, that is, the state of the dynamic system is governed by a parabolic equation together with an initial condition while the control is…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three dimensional bounded domain. The model is governed by a coupled system of…