Imperial College London
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DrAndrewWynn

Faculty of Engineering, Department of Aeronautics

Reader in Control and Optimization
 
 
 
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Contact

 

+44 (0)20 7594 5047a.wynn Website

 
 
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Location

 

340City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Fantuzzi:2017:10.1109/TAC.2017.2703927,
author = {Fantuzzi, G and Wynn, A and Goulart, P and Papachristodoulou, A},
doi = {10.1109/TAC.2017.2703927},
journal = {IEEE Transactions on Automatic Control},
pages = {6221--6236},
title = {Optimization with affine homogeneous quadratic integral inequality constraints},
url = {http://dx.doi.org/10.1109/TAC.2017.2703927},
volume = {62},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We introduce a new technique to optimize a linear cost function subject to an affine homogeneous quadratic integral inequality, i.e. the requirement that a homogeneous quadratic integral functional affine in the optimization variables is non-negative over a space of functions defined by homogeneous boundary conditions. Such problems arise in control and stability or input-to-state/output analysis of systems governed by partial differential equations (PDEs), particularly fluid dynamical systems. We derive outer approximations for the feasible set of a homogeneous quadratic integral inequality in terms of linear matrix inequalities (LMIs), and show that a convergent sequence of lower bounds for the optimal cost can be computed with a sequence of semidefinite programs (SDPs). We also obtain inner approximations in terms of LMIs and sum-of-squares constraints, so upper bounds for the optimal cost and strictly feasible points for the integral inequality can be computed with SDPs. We present QUINOPT, an open-source add-on to YALMIP to aid the formulation and solution of our SDPs, and demonstrate our techniques on problems arising from the stability analysis of PDEs.
AU  - Fantuzzi,G
AU  - Wynn,A
AU  - Goulart,P
AU  - Papachristodoulou,A
DO  - 10.1109/TAC.2017.2703927
EP  - 6236
PY  - 2017///
SN  - 0018-9286
SP  - 6221
TI  - Optimization with affine homogeneous quadratic integral inequality constraints
T2  - IEEE Transactions on Automatic Control
UR  - http://dx.doi.org/10.1109/TAC.2017.2703927
UR  - https://ieeexplore.ieee.org/document/7959080
UR  - http://hdl.handle.net/10044/1/48337
VL  - 62
ER  -
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