# Designing right endpoint boundary feedback stabilizers for the linearized Korteweg-de Vries equation using left endpoint boundary measurements

@article{Batal2018DesigningRE, title={Designing right endpoint boundary feedback stabilizers for the linearized Korteweg-de Vries equation using left endpoint boundary measurements}, author={Ahmet Batal and Turker Ozsari}, journal={arXiv: Optimization and Control}, year={2018} }

In this paper, we design an observer for the linearized Korteweg-de Vries (KdV) equation posed on a finite domain. We assume that there is a sensor at the left end point of the domain capable of measuring the first and second order boundary traces of the solution. Using only the partial information available, we construct Dirichlet-Neumann boundary controllers for the original system acting at the right endpoint so that the system becomes exponentially stable. Stabilization of the original… Expand

#### References

SHOWING 1-10 OF 30 REFERENCES

Pseudo-Backstepping and Its Application to the Control of Korteweg-de Vries Equation from the Right Endpoint on a Finite Domain

- Mathematics, Computer Science
- SIAM J. Control. Optim.
- 2019

This paper designs Dirichlet-Neumann boundary feedback controllers for the Korteweg-de Vries (KdV) equation which act at the right endpoint of the domain and introduces the pseudo-backstepping method which uses a pseudo-kernel that satisfies all but one desirable boundary condition. Expand

Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

- Mathematics, Computer Science
- 2015 American Control Conference (ACC)
- 2015

In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper. Expand

Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2013

The proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data to form a feedback control law for the Korteweg-de Vries equation. Expand

Boundary feedback stabilization of the Korteweg–de Vries–Burgers equation posed on a finite interval

- Mathematics
- 2016

Abstract This paper studies the boundary feedback stabilization problem of the Korteweg–de Vries–Burgers equation posed on a finite interval. A linear boundary feedback control law is proposed. Then… Expand

Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain

- Mathematics
- 1997

The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial… Expand

Output-feedback stabilization of the Korteweg-de Vries equation

- Mathematics, Computer Science
- 2016 24th Mediterranean Conference on Control and Automation (MED)
- 2016

The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and actuators located at different boundaries using backstepping method and introduces the nonlinear observer for the KdV equation. Expand

Controllability of the Korteweg-de Vries equation from the right Dirichlet boundary condition

- Mathematics, Computer Science
- Syst. Control. Lett.
- 2010

In this paper, we consider the controllability of the Korteweg–de Vries equation in a bounded interval when the control operates via the right Dirichlet boundary condition, while the left Dirichlet… Expand

Stabilization of linearized Korteweg-de Vries systems with anti-diffusion

- Computer Science, Mathematics
- 2013 American Control Conference
- 2013

In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve… Expand

Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping

- Mathematics, Computer Science
- Numerische Mathematik
- 2010

This work analysis of a fully-implicit numerical scheme for the critical generalized Korteweg–de Vries equation in a bounded domain with a localized damping term shows that the smallness of the initial condition leads to the uniform exponential decay of the energy associated to the scheme. Expand

Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain

- Mathematics
- 2009

It is known that the linear Korteweg–de Vries (KdV) equation with homogeneous Dirichlet boundary conditions and Neumann boundary control is not controllable for some critical spatial domains. In this… Expand