Related papers: Sidewise control of 1-d waves
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in a finite-dimensional set. In particular, we provide a complete characterization of…
The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the…
Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…
In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result, the novelty of…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the…
We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
Control variables provide an important means of controlling for endogeneity in econometric models with nonseparable and/or multidimensional heterogeneity. We allow for discrete instruments, giving identification results under a variety of…
In this paper we consider the problem of controlling pointwise, by means of a time dependent Dirac measure supported by a given point, a coupled system of two Korteweg-de Vries equations on the unit circle. More precisely, by means of…
A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial…
Solutions of a system of wave equations are constructed for both homogeneous and inhomogeneous Dirichlet boundary conditions at every regularity level. We prove that boundary observability, and thus boundary exact controllability, at some…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
The aim of this paper is to investigate the well-posedness of a class of boundary control and observation systems on a one dimensional spatial domain. We derive a necessary and sufficient condition characterizing the well-posedness of these…
This paper is devoted to studying the null and approximate controllability of two linear coupled parabolic equations posed on a smooth domain of R^N (N>1) with coupling terms of zero and first orders and one control localized in some…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…