Simulation studies on the boundary stabilization and disturbance rejection for fractional diffusion-wave equation

2004 ◽  
Author(s):  
Jinsong Liang ◽  
Yangquan Chen ◽  
R. Fullmer
Keyword(s):  
Wave Equation ◽  
Disturbance Rejection ◽  
Fractional Diffusion ◽  
Simulation Studies ◽  
Boundary Stabilization ◽  
Diffusion Wave

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

scholarly journals Boundary stabilization and disturbance rejection for a time fractional order diffusion-wave equation

2020 ◽  
Vol 53 (2) ◽  
pp. 3695-3700
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Wave Equation ◽  
Fractional Order ◽  
Disturbance Rejection ◽  
Boundary Stabilization ◽  
Diffusion Wave
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