Local rapid stabilization for a Korteweg–de Vries equation with a Neumann boundary control on the right

By Jean-Michel Coron, Qi Lu. 2013

86 citations recorded by the source corpus.

Abstract This paper is devoted to the study of the rapid exponential stabilization problem for a controlled Korteweg–de Vries equation on a bounded interval with homogeneous Dirichlet boundary conditions and Neumann boundary control at the right endpoint of the interval. For every noncritical length, we build a feedback control law to force the solution of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates, provided that the initial datum is small enough. Our approach relies on the construction of a suitable integral transform and can be applied to many other equations.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e186969d653c71f4dd51552118eb000eb5360c26

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Stabilization and controllability of first-order integro-differential hyperbolic equations (2015, methodology): “Finally, let us point out that Fredholm transformations ha ve lso been used to prove the exponential stabilization for a Korteweg-de Vries equation in [9] and for a Kuramoto-Si vashinsky equation in [10].”
Characterization by observability inequalities of controllability and stabilization properties (2018, background): “(t) = 2λe−2λT(T+ 1/2λ− t) if t∈ [T,T+ 1/2λ]. The function V(y) = hy,C−1 λ yi is a Lyapunov function (as noticed in [5]), and the feedback Kλyields exponential stability with rate −λ. We also refer to [6, 25] for developments on rapid stabilization. • Let us assume that Ais skew-adjoint, which is equ”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, methodology): “See, in particular, [1] for wave equations, [2] for compensating the distributed eﬀect of diﬀusion and counter-convection in Multi-Input and Multi-Output LTI systems, [6] for KdV equations, [7] for Kuramoto–Sivashinsky equations.”