Imperial College London
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ProfessorThomasParisini

Faculty of Engineering, Department of Electrical and Electronic Engineering

Chair in Industrial Control, Head of Group for CAP
 
 
 
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Contact

 

+44 (0)20 7594 6240t.parisini Website

 
 
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Location

 

1114Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Ascencio:2018:10.1109/TAC.2017.2757088,
author = {Ascencio, P and Astolfi, A and Parisini, T},
doi = {10.1109/TAC.2017.2757088},
journal = {IEEE Transactions on Automatic Control},
pages = {1943--1958},
title = {Backstepping PDE design: a convex optimization approach},
url = {http://dx.doi.org/10.1109/TAC.2017.2757088},
volume = {63},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sum-of-Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.
AU  - Ascencio,P
AU  - Astolfi,A
AU  - Parisini,T
DO  - 10.1109/TAC.2017.2757088
EP  - 1958
PY  - 2018///
SN  - 0018-9286
SP  - 1943
TI  - Backstepping PDE design: a convex optimization approach
T2  - IEEE Transactions on Automatic Control
UR  - http://dx.doi.org/10.1109/TAC.2017.2757088
UR  - https://ieeexplore.ieee.org/document/8052131
UR  - http://hdl.handle.net/10044/1/51032
VL  - 63
ER  -
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