James graduated from the University of Bristol in 2024 with an MEng Mechanical Engineering degree and a desire for more maths after spending 5 months designing a shoe testing robot for his master’s group project. Within this, he focused on optimisation of the passive mechanism’s geometry to accurately mimic running motion, drawing on experience gained from previous work exploring inverse problems in Non-Destructive Testing. Generally, his interests lie in the implementation of mathematical theory and coding to solve real world practical problems.

In his spare time, he is an over-ambitious cellist and competitively solves Rubik’s cubes.

Project title:
Fast machine learning for optimal feedback contro

Supervisor(s):
Sergey Dolgov

Project description:
Control theory can loosely be described as ‘poking’ a dynamical system to make it do what you want. Closed-loop feedback control determines this ‘poke’ based on the current state of the system, allowing for system stabilisation in the presence of external disturbances. There are many different techniques for designing a feedback control policy, one of these methods is Optimal Control: an infinite horizon minimisation of a value function combining trajectory error and control magnitude. In words, ‘What is the best overall control possible with the least effort?’ The resulting control signal is well understood and is defined by the solution of a Hamilton-JacobiBellman PDE. Unfortunately, this PDE becomes difficult to solve when system dynamics are non-linear. Additionally, the so-called ‘curse of dimensionality’ can come into play, making real-time implementation unfeasible for high-dimensional systems.

One solution to this is to replace the controller with a sufficiently pre-trained neural network (NN). Such a controller replaces the costly PDE solve with linear algebra, reducing computational complexity and improving scalability, allowing for applications to high-dimensional non-linear systems in real time on lightweight computing hardware. My research focuses on the development and application of NN-based optimal controllers, exploring different control formulations, implementations, network architecture and training methods.