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

DOI10.1137/18M1211933zbMath1411.93151arXiv1801.07206OpenAlexW2964100141MaRDI QIDQ4630682

Türker Özsarı, Ahmet Batal

Publication date: 23 April 2019

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.07206

zbMATH Keywords

feedback stabilizationbacksteppingKorteweg-de Vries equationboundary controllerpseudo-backstepping

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear systems in control theory (93C10)

Related Items (5)

Non-homogeneous boundary value problems for some KdV-type equations on a finite interval: a numerical approach ⋮ Stabilization of higher order Schrödinger equations on a finite interval. II ⋮ Output feedback stabilization of the linearized Korteweg-de Vries equation with right endpoint controllers ⋮ Stabilization of higher order Schrödinger equations on a finite interval. I ⋮ Boundary Stabilizability of the Linearized Compressible Navier--Stokes System in One Dimension by Backstepping Approach

Cites Work

• Unnamed Item
• Local rapid stabilization for a Korteweg-de Vries equation with a Neumann boundary control on the right
• Boundary feedback stabilization of the Korteweg-de Vries-Burgers equation posed on a finite interval
• Controllability of the Korteweg-de Vries equation from the right Dirichlet boundary condition
• Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping
• Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
• Semigroups of linear operators and applications to partial differential equations
• Exact boundary controllability of a nonlinear KdV equation with critical lengths
• Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation
• Global boundary stabilization of the Korteweg-de Vries-Burgers equation
• Control of a Korteweg-de Vries equation: a tutorial
• Boundary control of the Korteweg-de Vries-Burgers equation: further results on stabilization and well-posedness, with numerical demonstration
• Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
• Unique continuation and decay for the Korteweg-de Vries equation with localized damping
• Boundary Control of PDEs
• Exact Controllability of a Nonlinear Korteweg–de Vries Equation on a Critical Spatial Domain
• Local Exact Controllability and Stabilizability of the Nonlinear Schrödinger Equation on a Bounded Interval
• Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit
• Exact Boundary Controllability of the Korteweg--de Vries Equation
• A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain
• Stabilization of the Korteweg-de Vries equation with localized damping
• Boundary Feedback Stabilization of an Unstable Heat Equation
• On the uniform decay for the Korteweg–de Vries equation with weak damping
• Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition

This page was built for publication: Pseudo-Backstepping and Its Application to the Control of Korteweg--de Vries Equation from the Right Endpoint on a Finite Domain