A backstepping approach to adaptive error feedback regulator design for one-dimensional linear parabolic PIDEs

2021 ◽  
pp. 125310
Author(s):  
Wei-Wei Liu ◽  
Jun-Min Wang ◽  
Wei Guo
Keyword(s):  
Error Feedback ◽  
One Dimensional ◽  
Backstepping Approach ◽  
Feedback Regulator

Error feedback regulation for 1D anti-stable wave equation

2021 ◽  
pp. 014233122110592
Author(s):  
Zhiyuan Li ◽  
Feng-Fei Jin
Keyword(s):  
Wave Equation ◽  
Tracking Error ◽  
Feedback Regulation ◽  
Original System ◽  
Well Posedness ◽  
Error Feedback ◽  
One Dimensional ◽  
Internal Loop ◽  
Finite Dimensional ◽  
Uniformly Bounded

This paper is concerned with the boundary error feedback regulation for a one-dimensional anti-stable wave equation with distributed disturbance generated by a finite-dimensional exogenous system. Transport equation and regulator equation are introduced first to deal with the anti-damping on boundary and the distributed disturbance of the original system. Then, the tracking error and its derivative are measured to design an observer for both exosystem and auxiliary partial differential equation (PDE) system to recover the state. After proving the well-posedness of the regulator equations, we propose an observer-based controller to regulate the tracking error to zero exponentially and keep the states of all the internal loop uniformly bounded. Finally, some numerical simulations are presented to validate the effectiveness of the proposed controller.

VSS ERROR FEEDBACK REGULATOR FOR LINEAR SYSTEMS

2005 ◽  
Vol 38 (1) ◽  
pp. 706-711
Author(s):  
J. Rivera Domínguez ◽  
A.G. Loukianov ◽  
B. Castillo Toledo ◽  
V.A. Utkin
Keyword(s):  
Linear Systems ◽  
Error Feedback ◽  
Feedback Regulator
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