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.

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 Finite-time stabilization for fractional-order inertial neural networks with time varying delays

2022 ◽  
Vol 27 (1) ◽  
pp. 1-18
Author(s):  
Chaouki Aouiti ◽  
Jinde Cao ◽  
Hediene Jallouli ◽  
Chuangxia Huang
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Analytical Techniques ◽  
Control Algorithms ◽  
First Order ◽  
Inertial Neural Networks ◽  
Fractional Differential ◽  
Variable Substitution ◽  
Finite Time Stabilization ◽  
Delay Dependent

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results.

On the analysis and control of hyperbolic systems associated with vibrating networks

1994 ◽  
Vol 124 (1) ◽  
pp. 77-104 ◽  
Author(s):  
J. E. Lagnese ◽  
G. Leugering ◽  
E. J. P. G. Schmidt
Keyword(s):  
Hyperbolic Systems ◽  
Three Dimensional ◽  
Exact Controllability ◽  
General Linear Model ◽  
Regularity Of Solutions ◽  
Closed Loops ◽  
One Dimensional ◽  
First Order ◽  
And Control ◽  
First Time

In this paper a general linear model for vibrating networks of one-dimensional elements is derived. This is applied to various situations including nonplanar networks of beams modelled by a three-dimensional variant on the Timoshenko beam, described for the first time in this paper. The existence and regularity of solutions is established for all the networks under consideration. The methods of first-order hyperbolic systems are used to obtain estimates from which exact controllability follows for networks containing no closed loops.

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