相关论文: Final state observability estimates and cost-unifo…
The current article examines the approximate controllability problem for non-instantaneous impulsive fractional evolution equations of order $1<\alpha<2$ with state-dependent delay in separable reflexive Banach spaces. In order to establish…
We consider N independent quantum particles, in an infinite square potential well coupled to an external laser field. These particles are modelled by a system of linear Schr\"odinger equations on a bounded interval. This is a bilinear…
We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…
This manuscript is concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order $1<q<2$ in Banach spaces. As far as we know, few articles have investigated this issue. The…
We show that it is impossible to quantify the decay rate of a semi-uniformly stable operator semigroup based on sole knowledge of the spectrum of its infinitesimal generator. More precisely, given an arbitrary positive function $r$…
The average cost optimality is known to be a challenging problem for partially observable stochastic control, with few results available beyond the finite state, action, and measurement setup, for which somewhat restrictive conditions are…
We establish a separation principle for the output feedback stabilisation of state-affine systems that are observable at the stabilization target. Relying on control templates (recently introduced in [4]), that allow to approximate a…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include time-varying systems modeled with unbounded state-space operators acting…
We study (approximate) null-controllability of parabolic equations in $L_p(\mathbb{R}^d)$ and provide explicit bounds on the control cost. In particular we consider systems of the form $\dot{x}(t) = -A_p x(t) + \mathbf{1}_E u(t)$, $x(0) =…
We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space $X$. This is done by finite dimensional approximation. In particular we prove…
We establish existence, approximate controllability and optimal control of a class of impulsive non-local non-linear fractional dynamical systems in Banach spaces. We use fractional calculus, sectorial operators and Krasnoselskii fixed…
The present paper deals with the control problems governed by fractional non-instantaneous impulsive functional evolution equations with state-dependent delay involving Caputo fractional derivatives in Banach spaces. The main objective of…
In this paper, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1-D semiclassical cubic Schr\"odinger equation with two controls between two states…
We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate…
For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly…
This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions.…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
Strichartz estimates, well-posedness theory and long time behavior for (nonlinear) Schr\"odinger equations on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ are intensively studied in recent decades while the corresponding control…
Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A…