Optimization with affine homogeneous quadratic integral inequality constraints

Fantuzzi G, Wynn A, Goulart PJ, Papachristodoulou A (2017)

Publication Type: Journal article

Publication year: 2017

Journal

IEEETransactions on Automatic Control Institute of Electrical and Electronics Engineers (IEEE)

Book Volume: 62

Pages Range: 6221-6236

Journal Issue: 12

DOI: 10.1109/TAC.2017.2703927

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 nonnegative 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.

Authors with CRIS profile

Giovanni Fantuzzi

Involved external institutions

Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB) University of Oxford GB United Kingdom (GB)

How to cite

APA:

Fantuzzi, G., Wynn, A., Goulart, P.J., & Papachristodoulou, A. (2017). Optimization with affine homogeneous quadratic integral inequality constraints. IEEETransactions on Automatic Control, 62(12), 6221-6236. https://dx.doi.org/10.1109/TAC.2017.2703927

MLA:

Fantuzzi, Giovanni, et al. "Optimization with affine homogeneous quadratic integral inequality constraints." IEEETransactions on Automatic Control 62.12 (2017): 6221-6236.

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