Related papers: Boundary stabilization and observation of a multi-…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
In this paper, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an anti-stable stochastic heat equation with Neumann boundary actuation and unknown boundary…
In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…
In this paper, we develop a novel and simple adaptive control scheme for a one-dimensional unstable heat equation with unknown control coefficient. A new state observer is designed to estimate the system state, while a new update law is…
This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency…
The present work is devoted to the problem of boundary stabilization of the semilinear 1-D heat equation with nonlocal boundary conditions. The stabilizing controller is finite-dimensional, linear, given in an explicit form, involving only…
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…
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…
This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance.…
This paper is devoted to the study of the stability and stabilizability of heat equation in non-cylindrical domain. The interesting thing is that there is a class of initial values such that the system is no longer exponentially stable. The…
This paper is concerned with the stabilization of parallel-flow heat exchangers equation with boundary control and arbitrarily delayed observation. The observer and predictor-based method, developed by [B.Z. Guo, K.Y. Yang, Automatica,…
We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less…
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…
Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we…
We study global finite-dimensional observer-based stabilization of a semilinear 1D heat equation with globally Lipschitz semilinearity in the state variable. We consider Neumann actuation and point measurement. Using dynamic extension and…
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.…
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.…
We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…
This paper addresses the problem of feedback stabilization of a cascade of two heat equations that are coupled in the boundary conditions, the input being a boundary control for the first component of the cascade. Two distinct control input…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…