scholarly journals Null-controllability, exact controllability, and stabilization of hyperbolic systems for the optimal time

2020 ◽  
Author(s):  
Jean-Michel Coron ◽  
Hoai-Minh Nguyen
Keyword(s):  
Hyperbolic Systems ◽  
Exact Controllability ◽  
Null Controllability ◽  
Optimal Time

scholarly journals Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

2020 ◽  
Vol 26 ◽  
pp. 119 ◽  
Author(s):  
Jean-Michel Coron ◽  
Hoai-Minh Nguyen
Keyword(s):  
Finite Time ◽  
Nonlinear Boundary ◽  
Dimensional Space ◽  
Hyperbolic Systems ◽  
Optimal Time ◽  
Local Boundary ◽  
Quasilinear Hyperbolic Systems ◽  
Non Local ◽  
Linearized System ◽  
Finite Time Stabilization

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any time larger than the optimal time for the null controllability of the linearized system if the initial condition is sufficiently small. One of the key technical points is to establish the local well-posedness of quasilinear hyperbolic systems with nonlinear, non-local boundary conditions.

scholarly journals Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2×2 linear hyperbolic systems

2021 ◽  
Author(s):  
Long Hu ◽  
Guillaume Olive
Keyword(s):  
Finite Time ◽  
Hyperbolic Systems ◽  
Null Controllability ◽  
Convolution Theorem ◽  
Backstepping Method ◽  
Technical Point ◽  
One Dimensional ◽  
First Order ◽  
Minimal Time ◽  
Finite Time Stabilization

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2×2 linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.

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