Analysis and control of nonlinear feedback systems by differential positivity and dominance theory
Lead Research Organisation:
University of Cambridge
Department Name: Engineering
Abstract
The PhD project is rooted in Control engineering. The project will develop methods for analysis and control of nonlinear feedback systems, which are ubiquitous in natural and engineered systems.
The project is based on differential analysis and takes advantage of the novel theories of differential positivity and dominance. The aim of the project is to develop new tools for analysis and control design of systems which exhibit richly non-linear behaviour (e.g. bifurcations, discontinuities and oscillations) and are found throughout engineering, the physical sciences, the life sciences and the economic and social sciences.
Novel algorithms will be developed within the project to foster the use of differential positivity and dominance theory on several applications of interests, which include robotics, transportation, biological processes, and analysis and design of large-scale distributed systems.
The project is based on differential analysis and takes advantage of the novel theories of differential positivity and dominance. The aim of the project is to develop new tools for analysis and control design of systems which exhibit richly non-linear behaviour (e.g. bifurcations, discontinuities and oscillations) and are found throughout engineering, the physical sciences, the life sciences and the economic and social sciences.
Novel algorithms will be developed within the project to foster the use of differential positivity and dominance theory on several applications of interests, which include robotics, transportation, biological processes, and analysis and design of large-scale distributed systems.
Organisations
People |
ORCID iD |
| Fulvio Forni (Primary Supervisor) | |
| Dimitris Kousoulidis (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
| 1950140 | Studentship | EP/N509620/1 | 01/10/2017 | 30/09/2021 | Dimitris Kousoulidis |
| Description | We developed computational tools to support the research on monotone systems and differential positivity (a system analysis and synthesis framework recently developed in Cambridge). Monotonicity and differential positivity allow us to study systems with rich non-linear behaviour (e.g. bifurcations, discontinuities and oscillations) that are found throughout engineering, the physical sciences, the life sciences, and the economic and social sciences. Differential positivity provides a novel general framework that can be used for studying and reasoning about the behaviour of these systems in a unified way. With the computational tools that we have developed, we can numerically verify when a system is differentially positive and we can use the differential positivty framework in applications. We demonstrated how our numerical tools can be used to analyse and design a range of non-linear systems, including for example, non-linear multi-agent systems and robust switches. Our original objectives have been met, however we continue to work on scaling up this approach to bigger systems and networks of systems for the remainder of the award. Because of the theoretical nature of this research, we expect that the impact will be more on the long-term. Remarkably, our computational tools for differential positivity can also be adapted to the classical problems of stability and stabilisation of nonlinear systems. This opens new research directions that we will also be exploring in the following months. |
| Exploitation Route | These outcomes will be directly used by the project supervisor and his future students and collaborators. The computational tools developed in this research will be integrated into graduate courses offer in the Department of Engineering at the University of Cambridge. We are also hoping that our publications and application examples will seed interest in exploring these approaches by various domain experts and that, once it is fully published, our research toolbox software will lower the technical barrier required to do so. |
| Sectors | Electronics,Energy,Environment,Transport |
| Description | CDC 2019 Travel Award |
| Amount | € 325 (EUR) |
| Organisation | Institute of Electrical and Electronics Engineers (IEEE) |
| Sector | Learned Society |
| Country | United States |
| Start | 12/2019 |
| End | 12/2019 |
| Title | Toolbox for Polyhedral Computation |
| Description | Toolbox developed in parallel with our research for the duration of this award. It complements our research by providing computational tools for the study of differential positivity and stability. We plan to release this as an open source package by the end of the award's duration. |
| Type Of Technology | Software |
| Year Produced | 2021 |
| Impact | Was used to compute the examples in our two peer reviewed publications and for our third submitted paper. |
| Description | 2019 International Workshop on Control Engineering and Synthetic Biology |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Workshop attended by some of the world leading experts in the intersection of Synthetic Biology and Control theory. Got the opportunity to better understand the tools and methods currently used in the field and how our research can be used to improve them and networked with other postgraduate students. |
| Year(s) Of Engagement Activity | 2019 |
| URL | http://sysos.eng.ox.ac.uk/wiki/index.php/SynBioControl2019 |
| Description | 58th Conference on Decision and Control |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Presented our paper in the biggest conference in our field that has both a big academic and industry presence. We got the opportunity to formally present our work and received very good engangement from the audience of our session. We also got the chance to network with our peers and learn more about the latest developments in our field. |
| Year(s) Of Engagement Activity | 2019 |
| URL | https://cdc2019.ieeecss.org/ |
| Description | Emmanuel College Graduate Symposium |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Local |
| Primary Audience | Postgraduate students |
| Results and Impact | One day event organized by Emmanuel College's Middle Combination Room (MCR) that brought together all graduate students of the college, with fields ranging from History to Astrophysics and was also attended by senior members of the college. Presented our work and the more general problems that our field attempts to solve in an approachable way. |
| Year(s) Of Engagement Activity | 2019 |
| Description | IFAC World Congress 2020 |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Was turned to a virtual conference because of COVID-19. Created video presentation showcasing our work and was able to view many interesting talks by experts in the field. Unfortunately, the virtual layout limited opportunities for networking. |
| Year(s) Of Engagement Activity | 2020 |
| URL | https://www.ifac2020.org/ |
| Description | Personal Website |
| Form Of Engagement Activity | Engagement focused website, blog or social media channel |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | Personal academic website showcasing our work on this award and providing some high-level context of our plans; recorded around 200 unique visitors. |
| Year(s) Of Engagement Activity | 2020,2021 |
| URL | https://dkous.com/ |