Related papers: On Approximate Controllability of Impulsive Linear…
Inspired by normalizing flows, we analyze the bilinear control of neural transport equations by means of time-dependent velocity fields restricted to fulfill, at any time instance, a simple neural network ansatz. The L^1 approximate…
We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…
The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with…
A non-convex control system governed by a nonlinear impulsive evolution equation of Hilfer fractional order in a Banach space is considered. The existence of admissible state-control pair is established. Then the introduction of suitable…
We investigate the task of controlling ensembles of initial and terminal state vectors of parameter-dependent linear systems by applying parameter-independent open loop controls. Necessary, as well as sufficient, conditions for ensemble…
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is…
We explore further controllability problems through a standard least square approach. By setting up a suitable error functional $E$, and putting $m(\ge0)$ for the infimum, we interpret approximate controllability by asking $m=0$, while…
The paper is concerned with a class of stochastic evolution equations in Hilbert space with random coefficients driven by Teugel's martingales and an independent multi-dimensional Brownian motion and its optimal control problem. Here…
We study the small-time approximate controllability of bilinear Schr{\"o}dinger equations, where the drift is a magnetic Schr{\"o}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in…
We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
This work presents a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…
We prove a strong inapproximability result for the Balanced Minimum Evolution Problem. Our proof also implies that the problem remains NP-hard even when restricted to metric instances. Furthermore, we give a MST-based 2-approximation…
The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on the whole boundary. Our study is then…
In this paper, we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy-Neumann problems. First, we will obtain embedding results for weighted Sobolev spaces, that have proved decisive in…