相关论文: Reduction for constrained variational problems on …

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…

We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…

The goal of this paper is to extend to two-dimensional optimal control systems with scalar input the classical notion of Gaussian curvature of two-dimensional Riemannian surface using the Cartan's moving frame method. This notion was…

Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.

This paper deals with finding surfaces in $\mathbb{R}^3$ which are as close as possible to being flat and span a given contour such that the contour is a geodesic on the sought surface. We look for a surface which minimizes the total…

We consider optimal control problems of elliptic PDEs on hypersurfaces in 2- or 3-dimensional Euclidean space. The leading part of the PDE is given by the Laplace-Beltrami operator, which is discretized by finite elements on a polyhedral…

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

In optimal control problems, there exist different kinds of extremals, that is, curves candidates to be solution: abnormal, normal and strictly abnormal. The key point for this classification is how those extremals depend on the cost…

We study the exact boundary controllability of a nonlinear coupled system of two Korteweg-de Vries equations on a bounded interval. The model describes the interactions of two weakly nonlinear gravity waves in a stratified fluid. Due to the…

We derive an optimal control formulation for a nonholonomic mechanical system using the nonholonomic constraint itself as the control. We focus on Suslov's problem, which is defined as the motion of a rigid body with a vanishing projection…

We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…

We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler's equations, concentrating on the case when the moment of inertia is zero. We prove that the only motions that lead to total collisions are self-similar…

This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…

In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie…

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…