A constriction in the neural tube at the junction of the midbrain and hindbrain is a conserved feature of vertebrate embryos. The constriction is a defining feature of the midbrain-hindbrain boundary (MHB), a signaling center that patterns the adjacent midbrain and rostral hindbrain and forms at the junction of two gene expression domains in the early neural plate: an anterior otx2/wnt1 positiv...

We consider the Korteweg{de Vries{Burgers (KdVB) equation on the interval 0; 1]. Motivated by poor decay rates of a recently proposed control law by Liu and Krstic which keeps some of the boundary conditions as homogeneous, we propose a strengthened set of feedback boundary conditions. We establish stability properties of the closed{loop system and illustrate the performance improvement by a si...

We consider a stabilization problem for abstract second-order evolution equations with dynamic boundary feedback laws with a delay and distributed structural damping. We prove an exponential stability result under a suitable condition between the internal damping and the boundary laws. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay es...

We consider the Korteweg–de Vries–Burgers (KdVB) equation on the interval [0,1]. Motivated by simulations resulting in modest decay rates with recently proposed control laws by Liu and Krstic which keeps some of the boundary conditions as homogeneous, we propose a strengthened set of feedback boundary conditions. We establish stability properties of the closed-loop system, prove well-posedness ...

Gain and time-constant factors shift the inverse process relative to its feedback controller. A new robustness plot cross-graphs these shift factors that take the loop to the stability boundary as a function of frequency.

This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steadystate to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of gene...

We investigate the boundary stabilization of a particular subset of 3×3 linear hyperbolic systems with varying coefficients on a bounded domain. The system is underactuated since only one of the three hyperbolic PDEs is actuated at the boundary. The setup considered in the paper occurs in control of multiphase flows on oil production systems. We use a backstepping approach to design a full-stat...

We consider a control system for a Korteweg-de Vries equation with homogeneous Dirichlet boundary conditions and Neumann boundary control. We address the rapid exponential stabilization problem. More precisely, we build some feedback laws forcing the solutions of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates. We also perform some numerical computa...

Abstract: We study a dynamic system described by the Kuramoto-Sivashinsky equation with an external excitation f posed on a finite domain. Firstly it shows that under the given boundary feedback conditions it admits a unique solution and the solution is stable. Secondly it proves that if the external excitation f is a time periodic function, then the system under the boundary conditions admits ...