Related papers: Geometric structure-preserving optimal control of …
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
This work addresses the optimal control of multibody systems being actuated with control forces in order to find a dynamically feasible minimum-energy trajectory of the system. The optimal control problem and its constraints are integrated…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in…
In this work, asymptotically stable state estimation schemes are proposed for rigid body motion, using the framework of geometric mechanics. Rigorous stability analyses of the estimation schemes presented here guarantee the nonlinear…
In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…
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…
A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…
The general topic of the present paper is to study the conservation for some structural property of a given problem when discretising this problem. Precisely we are interested with Lagrangian or Hamiltonian structures and thus with…
In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…
Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…
In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We…
We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the…
We describe the main ingredients needed to create, from the smooth lagrangian density, a variational principle for discrete motions of a discrete rod, with corresponding conserved Noether currents. We describe all geometrical objects in…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…