Related papers: Optimal Control for Burgers Equation using Particl…
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,…
We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…
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 propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…