Related papers: Linear multistep methods for optimal control probl…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
A review of the most popular Linear Multistep (LM) Methods for solving Ordinary Differential Equations numerically is presented. These methods are first derived from first principles, and are discussed in terms of their order, consistency,…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
We study a pointwise tracking optimal control problem for the stationary Navier--Stokes equations; control constraints are also considered. The problem entails the minimization of a cost functional involving point evaluations of the state…
This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…
In this article, a class of optimal control problems of differential equations with delays are investigated for which the associated Hamilton-Jacobi-Bellman (HJB) equations are nonlinear partial differential equations with delays. This type…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy…
In this article, two methods for solving mean-field type optimal control problems are proposed and investigated. The two methods are iterative methods: at each iteration, a Hamilton-Jacobi-Bellman equation is solved, for a terminal…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
It is shown that for a parabolic problem with maximal $L^p$-regularity (for $1<p<\infty$), the time discretization by a linear multistep method or Runge--Kutta method has maximal $\ell^p$-regularity uniformly in the stepsize if the method…
A hyperbolic system approach is proposed for robust computation of anisotropic diffusion equations that appear in quasineutral plasmas. Though the approach exhibits merits of high extensibility and accurate flux computation, the…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…