Farkas' lemma is an ubiquitous tool in optimisation, as it provides necessary and sufficient conditions to have $b \in A(P)$, where $P$ is a closed convex cone, $A$ is a …
In this article, we explore connections between two stabilization methods: Gramian stabilization and backstepping (and more generally F-equivalence). These methods are related to …
Analysing reachability associated to a control system is a subtle issue, especially for infinitedimensional dynamics, and when controls are subject to bounded constraints. We …
In this paper we address the existence of a Fredholm backstepping transformation for self-adjoint operators A. We prove, under assumptions on the control operator B and A, that …
Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. …
It is customary to design a controlled system in such a way that, whatever the chosen control satisfying the constraints, the system does not enter so-called unsafe regions. This …
Fredholm-type backstepping transformation, introduced by Coron and Lü, has become a powerful tool for rapid stabilization with fast development over the last decade. Its strength …
We consider the internal control of linear parabolic equations through on-off shape controls, with a prescribed maximal measure. We establish small-time approximate controllability …
We give convergence and cost estimates for a data-driven system identification method: given an unknown dynamical system, the aim is to recover its vector field and its flow from …
We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption …