Related papers: Finite-approximate controllability of evolution sy…
In this paper we derive for a controlled stochastic evolution system on a Hilbert space sufficient conditions for optimality. Our result is derived by using its so-called adjoint backward stochastic evolution equation.
We establish necessary and sufficient conditions for viability of evolution inclusions with locally monotone operators in the sense of Liu and R\"ockner [J. Funct. Anal., 259 (2010), pp. 2902-2922]. This allows us to prove wellposedness of…
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…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
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 article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution,…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
We show that a bilinear control system is approximately controllable if and only if it is controllable in $\mathbb{R}^{n}\setminus\{0\}$. We approach this problem by looking at the foliation made by the orbits of the system, and by showing…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…
We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally…
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
In this paper we study the approximate controllability of fractional partial differential equations associated with the so-called Hilfer type time fractional derivative and a non-negative selfadjoint operator $A$ with a compact resolvent on…