Sum-of-Squares Approach to Global Stability and Control of Fluid Flows
Lead Research Organisation:
University of Oxford
Department Name: Engineering Science
Abstract
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Publications
Ahmadi M
(2019)
A framework for input-output analysis of wall-bounded shear flows
in Journal of Fluid Mechanics
Zhang X
(2015)
A real-time control framework for smart power networks: Design methodology and stability
in Automatica
Papachristodoulou A
(2015)
Advances in computational Lyapunov analysis using sum-of-squares programming
in Discrete and Continuous Dynamical Systems - Series B
Anghel M
(2013)
Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis
in IEEE Transactions on Circuits and Systems I: Regular Papers
Zheng Y
(2019)
Chordal decomposition in operator-splitting methods for sparse semidefinite programs
in Mathematical Programming
Raman D
(2016)
Delineating Parameter Unidentifiabilities in Complex Models
Raman DV
(2017)
Delineating parameter unidentifiabilities in complex models.
in Physical review. E
Ahmadi M
(2016)
Dissipation inequalities for the analysis of a class of PDEs
in Automatica
Zhang X
(2018)
Distributed Control for Reaching Optimal Steady State in Network Systems: An Optimization Approach
in IEEE Transactions on Automatic Control
Zheng Y
(2017)
Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming Using ADMM
in IEEE Control Systems Letters
Zheng Y
(2019)
Fast ADMM for Sum-of-Squares Programs Using Partial Orthogonality
in IEEE Transactions on Automatic Control
Lasagna D
(2016)
Flow regimes in a simplified Taylor-Couette-type flow model
in European Journal of Mechanics - B/Fluids
Hancock E
(2013)
Generalised absolute stability and sum of squares
in Automatica
Valmorbida G
(2015)
Introducing INTSOSTOOLS: A SOSTOOLS plug-in for integral inequalities
Prescott TP
(2014)
Layered decomposition for the model order reduction of timescale separated biochemical reaction networks.
in Journal of theoretical biology
Valmorbida G
(2017)
Nonlinear Static State Feedback for Saturated Linear Plants via a Polynomial Approach
in IEEE Transactions on Automatic Control
Raman D
(2016)
On the performance of nonlinear dynamical systems under parameter perturbation
in Automatica
Fantuzzi G
(2017)
Optimization With Affine Homogeneous Quadratic Integral Inequality Constraints
in IEEE Transactions on Automatic Control
Chernyshenko SI
(2014)
Polynomial sum of squares in fluid dynamics: a review with a look ahead.
in Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Description | The aim of this project is to understand the properties of systems described by partial differential equations, such as the ones describing the motion of fluids, using computational techniques that do not need to solve these equations. A major milestone was to be able to computationally verify that certain integral inequalities hold. We have developed a method to do that and this opens the way to apply this method to a number of problems related to dynamical systems in areas such as fluid mechanics, chemical reactions and heat transfer, all described by partial differential equations. This method is being used by other academics to answer questions about their models, without the need to simulate them. |
Exploitation Route | By using the software package we developed (intsostools, https://github.com/gvalmorbida/INTSOSTOOLS) and also using our mathematical results. |
Sectors | Environment |
URL | https://www.imperial.ac.uk/aeronautics/fluiddynamics/sumofsquares/index.php |
Description | The project's aim is to find a way to understand mathematical models of physical systems described by Partial Differential Equations (PDEs) without solving these PDEs. The results we obtained are theoretical and mathematical in nature but we expect that in the future they will be used to result in societal and economical impact. Especially since the final publication of the JFM paper, we expect that industry will be interested in adopting some of our techniques to provide provable bounds on properties of their designs. |
First Year Of Impact | 2019 |
Sector | Environment |
Description | Collaboration on Sum of Squares and Fluid Mechanics with UCSB |
Organisation | University of California, Santa Barbara |
Country | United States |
Sector | Academic/University |
PI Contribution | Collaboration, exchange of ideas and knowledge |
Collaborator Contribution | Collaboration, exchange of ideas and knowledge |
Impact | Ongoing. |
Start Year | 2013 |