A monotone circuit theory for control and learning in physical networks
Summary
Over the last decade, the rising energy intensiveness of machine learning has spurred a host of innovations in alternative computing architectures. Among them are in-memory computing, where computational and memory devices are collocated, and spiking neural networks, which draw inspiration from the spiking behaviour of biological nervous systems. Such systems use a mix of analog and digital circuits, and the development of a rigorous theory of design and control of such systems requires revisiting the fundamentals of nonlinear circuit and control theory.
Supervisor
Dr Thomas Chaffey.
Research location
Electrical and Computer Engineering
Synopsis
The projects draws upon the mathematical language of monotone operator theory as a common abstraction of ideas in nonlinear control theory, circuit theory, optimization and neural networks, to develop such a theory of design and control.
The project comprises several subprojects:
- Non-equilibrium stability theory: current input/output stability analysis is either performed with respect to an equilibrium, which is tractable but restrictive in the context of non-equilibrium behaviours such as spiking of a neuron, or with respect to an arbitrary reference, which lacks tractable verification tools. The project aims to develop a theory of stability of properties in between these two extremes. The key tool will be the Scaled Relative Graph, a graphical tool allowing Nyquist-type analysis of nonlinear systems.
- Circuit realisation of equilibrium and mixed-equilibrium networks: this project will develop a theory of circuit realisation for particular classes of neural networks, so-called equilibrium networks, and use these as building blocks for systems which exhibit non-equilibrium behaviour such as spiking, drawing on tools from switched and time-varying system theory. Training of such networks will be studied, using hardware-accelerated methods of computing gradients, and their efficacy as machine learning structures will be tested.
- Optimal control of monotone networks: this project will explore the use of monotone splitting algorithms, from the theory of large-scale convex optimisation, in optimal control problems where the plant has the structure of a monotone circuit. Applications in MPC and learning will be explored.
Additional information
Offering:
Multiple scholarships are currently available in the areas stipulated above. The successful candidate will be awarded a scholarship for 3.5 years at the RTP stipend rate (currently $41,753 in 2025) subject to satisfactory academic performance. International applicants will receive a tuition fee scholarship for upto 3.5 years.
Successful candidates:
- Must have a have a Bachelors degree (1st class honours or equivalent) or a Master's degree in Engineering, Mathematics, Computer Science or a related field, with experience in control theory.
How to apply:
To apply, please email Dr Thomas Chaffey the following:
- CV,
- Transcript, and
- A brief cover letter
Want to find out more?
Opportunity ID
The opportunity ID for this research opportunity is 3625
