Related papers: Boundary Feedback Control of Unstable Heat Equatio…
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the…
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it…
We consider the null-controllability of a non-local heat equation by interior $L^2(\Omega)$ controls. We confirm a conjecture of Lissy and Zuazua by showing that it is enough to assume that the kernel $k(x,\xi)$ is symmetric and…
This article concerns the nonlinear Korteweg-de Vries equation with boundary time-delay feedback. Under appropriate assumption on the coefficients of the feedbacks (delayed or not), we first prove that this nonlinear infinite dimensional…
We present a stabilizing output-feedback controller for nonlinear finite and infinite-dimensional control systems governed by monotone operators that respects given input constraints. In particular, we show under a detectability-like…
We discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_\infty$-output feedback controllers which stabilize the infinite dimensional system exponentially…
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…
A sliding-mode-based adaptive boundary control law is proposed for a class of uncertain thermal reaction-diffusion processes subject to matched disturbances. The disturbances are assumed to be bounded, but the corresponding bounds are…
The assessment of the thermal properties of walls is essential for accurate building energy simulations that are needed to make effective energy-saving policies. These properties are usually investigated through in-situ measurements of…
This paper is concerned with a feedback approximate controllability problem of blowup points for the heat equation. We show that the system is approximately controllable for blowup points with feedback controls and the feedback operator is…
We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…
We consider the heat equation with dynamic bounary conditions involving gradient terms in a bounded domain. In this paper we study the cost of approximate controllability for this equation. Combining new developed Carleman estimates and…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…
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.…
This paper addresses the problem of stabilization of $1$-D parabolic equations with destabilizing terms and Dirichlet boundary disturbances. By using the method of backstepping and the technique of splitting, a boundary feedback controller…
This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…
In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination…
We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time…