Related papers: Reduction for constrained variational problems on …
- We discuss the approximation of distributed null controls for partial differential equations. The main purpose is to determine an approximation of controls that drives the solution from a prescribed initial state at the initial time to…
A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
This paper discusses the energy optimal control problem for the class of quantum systems that possess dynamical symmetry of SU(1,1), which are widely studied in various physical problems in the quantum theory. Based on the maximum principle…
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…
This paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…