Altmetric

Optimization with affine homogeneous quadratic integral inequality constraints

File Description SizeFormat 
07959080.pdfPublished version657.8 kBAdobe PDFView/Open
Title: Optimization with affine homogeneous quadratic integral inequality constraints
Authors: Fantuzzi, G
Wynn, A
Goulart, P
Papachristodoulou, A
Item Type: Journal Article
Abstract: 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.
Issue Date: 26-Jun-2017
Date of Acceptance: 26-Apr-2017
URI: http://hdl.handle.net/10044/1/48337
DOI: https://dx.doi.org/10.1109/TAC.2017.2703927
ISSN: 1558-2523
Publisher: IEEE
Start Page: 6221
End Page: 6236
Journal / Book Title: IEEE Transactions on Automatic Control
Volume: 62
Issue: 12
Copyright Statement: © 2017 IEEE. This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: 1864077
Keywords: Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Integral inequalities
partial differential equations (PDEs)
semidefinite programming
sum-of-squares optimization
OF-SQUARES APPROACH
ENERGY-DISSIPATION
VARIATIONAL BOUNDS
INCOMPRESSIBLE FLOWS
SHEAR-FLOW
PROGRAMS
SYSTEMS
PDES
math.OC
35A23, 90C22
0906 Electrical And Electronic Engineering
0102 Applied Mathematics
0913 Mechanical Engineering
Industrial Engineering & Automation
Publication Status: Published
Appears in Collections:Faculty of Engineering
Aeronautics



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx