Flatness for a strongly degenerate 1-D parabolic equation

We consider the degenerate equation ∂ t f ( t , x ) - ∂ x x α ∂ x f ( t , x ) = 0 , on the unit interval x ∈ ( 0 , 1 ) , in the strongly degenerate case α ∈ [ 1 , 2 ) with adapted boundary conditions at x = 0 and boundary control at x = 1 . We use the flatness approach to construct explicit controls...

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Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2016-12, Vol.28 (4), p.1-22, Article 28
Main Author: Moyano, Iván
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary control
Communications Engineering
Control
Control systems
Flatness
Intervals
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Original Article
Partial differential equations
Robotics
Steering
Systems Theory
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Summary:We consider the degenerate equation ∂ t f ( t , x ) - ∂ x x α ∂ x f ( t , x ) = 0 , on the unit interval x ∈ ( 0 , 1 ) , in the strongly degenerate case α ∈ [ 1 , 2 ) with adapted boundary conditions at x = 0 and boundary control at x = 1 . We use the flatness approach to construct explicit controls in some Gevrey classes steering the solution from any initial datum f 0 ∈ L 2 ( 0 , 1 ) to zero in any time T > 0 .
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-016-0180-7