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
Raman D
(2016)
Delineating Parameter Unidentifiabilities in Complex Models
Zhang X
(2016)
Real-time active and reactive power regulation in power systems with tap-changing transformers and controllable loads
in Sustainable Energy, Grids and Networks
Lasagna D
(2016)
Sum-of-Squares approach to feedback control of laminar wake flows
Valmorbida G
(2016)
Stability Analysis for a Class of Partial Differential Equations via Semidefinite Programming
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
Ahmadi M
(2016)
Dissipation inequalities for the analysis of a class of PDEs
in Automatica
Valmorbida G
(2017)
Nonlinear Static State Feedback for Saturated Linear Plants via a Polynomial Approach
in IEEE Transactions on Automatic Control
Valmorbida G
(2017)
Region of attraction estimation using invariant sets and rational Lyapunov functions
in Automatica
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 |