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
(2016)
Dissipation inequalities for the analysis of a class of PDEs
in Automatica
Ahmadi M
(2017)
Safety verification for distributed parameter systems using barrier functionals
in Systems & Control Letters
Ahmadi M
(2019)
A framework for input-output analysis of wall-bounded shear flows
in Journal of Fluid Mechanics
Anderson J
(2012)
Robust nonlinear stability and performance analysis of an F/A-18 aircraft model using sum of squares programming
in International Journal of Robust and Nonlinear Control
Anghel M
(2013)
Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis
in IEEE Transactions on Circuits and Systems I: Regular Papers
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
Fantuzzi G
(2017)
Optimization With Affine Homogeneous Quadratic Integral Inequality Constraints
in IEEE Transactions on Automatic Control
Hancock E
(2013)
Generalised absolute stability and sum of squares
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 |