Related papers: Sub-Finsler structures from the time-optimal contr…
A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions…
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
We study the time optimal control problem with a general target $\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the…
The goal of this paper is to describe a method to solve a class of time optimal control problems which are equivalent to finding the sub-Riemannian minimizing geodesics on a manifold M. In particular, we assume that the manifold M is acted…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on…
In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control region. We establish the positive result thanks…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
The authors found extremals of arbitrary left-invariant sub-Finsler metric on the Engel group defined by a distribution of rank two. They use for this the Pontryagin Maximum Principle for the corresponding time-optimal problem in…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary…
A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the…
We study convexity properties of distance functions in Finsler unitary groups, where the Finsler structure is defined by translation of the $p$-Schatten norm on the Lie algebra. As a result we prove the existence of circumcenters for sets…