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The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
The global null controllability of stochastic semilinear parabolic equations with globally Lipschitz nonlinearities has been addressed in recent literature. However, there are no results concerning their numerical approximation and the…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on…
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…
In this paper, we study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints. Applying the terminal perturbation method and Ekeland's…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
We consider a $2\times 2$ system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse…
The paper is devoted to the optimal control of a system with two time-scales, in a regime when the limit equation is not of averaging type but, in the spirit of Wong-Zakai principle, it is a stochastic differential equation for the slow…
This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…
In the development of controllability and inverse problem results for semi-discrete systems, by using Carleman estimates, it is required to estimate of the discrete operators applied to Carleman weight functions. This work aims to establish…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this paper we consider a constrained parabolic optimal control problem. The cost functional is quadratic and it combines the distance of the trajectory of the system from the desired evolution profile together with the cost of a control.…
In this paper, we prove a Carleman estimate for fully-discrete approximations of parabolic operators in which the discrete parameters $h$ and $\triangle t$ are connected to the large Carleman parameter. We use this estimate to obtain…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
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…