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Control of underwater vehicles in inviscid fluids: I. Irrotational flows
In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through ...
Long time versus steady state optimal control
This paper analyzes the convergence of optimal control problems for an evolution equation in a finite time-horizon [0, T] toward the limit steady state ones as T ?8. We focus on linear problems. We first consider linear ...
Schrödinger operators with boundary singularities: Hardy inequality, Pohozaev identity and controllability results
The aim of this paper is two folded. Firstly, we study the validity of a Pohozaev-type identity for the Schrödinger operator A λ:=-δ-λ/|x| 2, λ∈R, in the situation where the origin is located on the boundary of a smooth ...
A systematic method for building smooth controls for smooth data
We prove a regularity result for an abstract control problem z' = Az + Bv with initial datum z(0) = z0 in which the goal is to determine a control v such that z(T) = 0. Under standard admissibility and observability ...
Some controllability results for the 2D Kolmogorov equation
In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the right-hand side of the equation, located on a subdomain, that ...