相关论文: A boundary control problem associated to the Rayle…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
Traffic control is at the core of research in transportation engineering because it is one of the best practices for reducing traffic congestion. It has been shown in recent years that the traffic control problem involving…
Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through…
This paper recalls a partial differential equations system, which is the linearization of a recognized fluid-elasticity interaction three-dimensional model. A collection of regularity results for the traces of the fluid variable on the…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Amp\`ere type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this…
We consider parabolic equations on bounded smooth open sets $\Om\subset \R^N$ ($N\ge 1$) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator $\mathscr{L} \coloneqq - \Delta + (-\Delta)^{s}$…
A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove…
We construct a determining form for the 2D Rayleigh-B\'enard (RB) system in a strip with solid horizontal boundaries, in the cases of no-slip and stress-free boundary conditions. The determining form is an ODE in a Banach space of…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a…
In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…
In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…
We prove existence and regularity for the solutions to a Cahn-Hilliard system describing the phenomenon of phase separation for a material contained in a bounded and regular domain. Since the first equation of the system is perturbed by the…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
In this work we provide a first order sensitivity analysis of some parameterized stochastic optimal control problems. The parameters can be given by random processes. The main tool is the one-to-one correspondence between the adjoint states…