Related papers: Analysis and approximations of an optimal control …
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin…
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…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…
In this paper we study optimal control problems with either fractional or regional fractional $p$-Laplace equation, of order $s$ and $p\in [2,\infty)$, as constraints over a bounded open set with Lipschitz continuous boundary. The control,…
In this article, we are concerned about the velocity tracking optimal control problem for 3D critical convective Brinkman-Forchheimer equations defined on a simply connected bounded domain $\mathbb{D}\subset\mathbb{R}^3$ with…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits…
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, including the stochastic Allen-Cahn equation, driven by an…
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear part of the target system is usually discretized implicitly,…
As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the…
In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique.…
In this study, we consider an optimal control problem driven by a stochastic differential equation with state constraints. Here, the state constraints mean the constraints about the path of state. In order to show the maximum principe for…