Related papers: On feedback stabilisation for the Cahn-Hilliard eq…
Feedback stabilization of an ensemble of non interacting half spins described by Bloch equations is considered. This system may be seen as a prototype for infinite dimensional systems with continuous spectrum. We propose an explicit…
In this article, we explore the feedback stabilization of a viscous Burgers equation around a non-constant steady state using localized interior controls and then develop error estimates for the stabilized system using finite element…
We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the…
We present a formulation of measurement-based feedback control of a single quantum particle in one spatial dimension. An arbitrary linear combination of the position and momentum of the particle is continuously monitored, and feedback…
In this paper we consider the problem of stabilization and tracking of desired state trajectory for a wide range of nonlinear control problems with disturbances. We present the sufficient conditions for the existence of $C^k$ state feedback…
The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
Quantum feedback control is a technology which can be used to drive a quantum system into a predetermined eigenstate. In this article, sufficient conditions for the experiment parameters of a quantum feedback control process of a homodyne…
In this paper, we study the long-time behavior of a stochastic heat equation with multiplicative noise and localized control. We begin by analyzing the uncontrolled dynamics and derive explicit decay rates for both mean-square and almost…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we…
In this paper, we consider a two-qubit system undergoing continuous-time measurements. In presence of multiple channels, we provide sufficient conditions on the continuous feedback control law ensuring almost sure exponential convergence to…
We study convergence and stability properties of control-affine systems. Our considerations are motivated by the problem of stabilizing a control-affine system by means of output feedback for states in which the output function attains an…
Feedback optimization refers to a class of methods that steer a control system to a steady state that solves an optimization problem. Despite tremendous progress on the topic, an important problem remains open: enforcing state constraints…
We present a novel continuous-time control strategy to exponentially stabilize an eigenstate of a Quantum Non-Demolition (QND) measurement operator. In open-loop, the system converges to a random eigenstate of the measurement operator. The…
In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control.…
A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…
We study the output feedback exponential stabilization for a 1-d wave PDE with dynamic boundary. With only one measurement, we construct an infinite-dimensional state observer to trace the state and design an estimated state based…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…