相关论文: Boundary output feedback stabilisation for 2-D and…

In recently proposed stabilisation techniques for parabolic equations, a crucial role is played by a suitable sequence of oblique projections in Hilbert spaces, onto the linear span of a suitable set of M actuators, and along the subspace…

This paper considers the backstepping state feedback control of coupled linear parabolic PDEs with spatially varying coefficients and bilateral actuation. By making use of the folding technique, a system representation with unilateral…

This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…

The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…

In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…

A popular approach to designing finite-dimensional boundary controllers for partial differential equations (PDEs) is to decompose the PDE into independent modes and focus on the dominant ones while neglecting highly damped residual modes.…

An explicit output-feedback boundary feedback law is introduced that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an $n$-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only…

The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and an actuator located at different boundaries (anti collocated set-up) using backstepping method. The feedback control…

We study the output feedback exponential stabilization of a one-dimensional unstable wave equation, where the boundary input, given by the Neumann trace at one end of the domain, is the sum of the control input and the total disturbance.…

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of various classes of damped nonlinear wave equations. Specifically, stabilization the zero steady state solution of initial boundary value…

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.…

In this paper we present an abstract maximal $L^p$-regularity result up to $T = \infty$, that is tuned to capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject to finite dimensional,…

This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients. Thereby, the coupling in the PDE is in-domain and at the…

This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations,…

This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…

This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…

We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…

Here we design boundary feedback stabilizers to unbounded trajectories, for semi-linear stochastic heat equation with cubic non-linearity. The feedback controller is linear, given in a simple explicit form and involves only the…

We describe a general multiplier method to obtain boundary stabilization of the wave equation by means of a (linear or quasi-linear) Neumann feedback. This also enables us to get Dirichlet boundary control of the wave equation. This method…

The present paper provides a solution in the affirmative to a recognized open problem in the theory of uniform stabilization of 3-dimensional Navier-Stokes equations in the vicinity of an unstable equilibrium solution, by means of a…