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We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find…
We consider a physical system constituted by a finite chain of point masses consecutively linked by linear springs and dashpots. At one of the end points acts an external control force aligned with the chain and the system is observable by…
In this paper we deal with the compressible Navier-Stokes equations with a friction term in one dimension on an interval. We study the exact controllability properties of this equation with general initial condition when the boundary…
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
This work is concerned with the possibility of proving the boundary null controllability for the degenerate wave equation, developing the asymptotic analysis of a suitable family of state-control pairs $((u_\varepsilon ,…
We consider a linear viscoelastic system of Maxwell-Boltzmann type. Hence, viscosity contributes a memory term to the elastic equation. The system is controlled via the traction exerted on a part $\Gamma_1$ of the boundary of the body. We…
We study the boundary controllability problem for a multilayer Rao-Nakra sandwich beam. This beam model consists of a Rayleigh beam coupled with a number of wave equations. We consider all combinations of clamped and hinged boundary…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
A new class of control problems is discussed - homeostasis control. Homeostasis control problems can be considered as control problems with a given target set, in particular, as a problem of stabilizing the values of some target function,…
We examine the spectrum of small perturbations around global and local (gauge) abelian vortices, using simple numerical matrix techniques. The results are of interest for both cosmic strings and for their condensed matter analogues,…
We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…
These notes provide a survey of recent results and open problems on the boundary control of moving sets. Motivated by the control of an invasive biological species, we consider a class of optimization problems for a moving set $t\mapsto…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a…
This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the…
In this paper, we consider the problem of tuning the edge weights of a networked system described by linear time-invariant dynamics. We assume that the topology of the underlying network is fixed and that the set of feasible edge weights is…