A car’s self-driving system hesitates at a junction because it cannot tell whether the gust of wind or the flicker of a pedestrian’s shadow is a genuine hazard. This project tackles that fundamental problem: how to control a system—a vehicle, a power grid, a financial market—when the signals it receives are constantly corrupted by noise and random disturbances. Traditional control methods treat this noise as a nuisance to be filtered out, which often leads to brittle, unreliable behaviour in the real world. The researcher proposes flipping that logic: treat uncertainty as useful information, not a bug. By building a mathematical framework that continuously optimises a probability distribution of control inputs—rather than trying to force the system into a single predicted state—the work aims to produce control strategies that adapt gracefully to unpredictable environments. The project is primarily theoretical, laying the mathematical and computational groundwork over 12 months. If successful, it could eventually make autonomous vehicles safer in rain or fog, help energy storage systems balance supply against erratic demand, and stabilise financial trading algorithms during volatile swings.
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In this small grant project, I will take the first steps toward developing a continuous-time probabilistic control framework to address the challenges of manipulating stochastic systems. The proposed project is motivated by the need to develop robust methods for controlling practical stochastic systems to advance real-world applications. While this has been successfully demonstrated in idealised, isolated settings, many real-world systems, such as autonomous vehicles and energy systems, operate in open environments where external factors introduce uncertainties such as noise and disturbances. These uncertainties challenge reliable system control, scalability of stochastic systems, and their accurate operation. Traditional control strategies often assume idealised conditions, leading to incomplete system characterisations and compromising the reliability and precision of control strategies. By treating these uncertainties as sources of valuable information rather than problems to be eliminated, this project aims to develop an innovative probabilistic approach that effectively characterises system dynamics and integrates uncertainties as an essential part of the control solution, enabling robust control strategies for real-world stochastic systems. The framework will offer a principled approach to managing uncertainty in dynamic and partially controllable systems. Specifically, it will establish the mathematical foundation for continuous-time probabilistic control by optimising a continuously evolving probability density function of control inputs rather than directly shaping the probabilistic evolution of system states. It will also develop computational methods for real-time implementation in high-dimensional stochastic systems. By leveraging recent advancements in probabilistic estimation and optimal transport, the framework will enable adaptive and timely control. Simulation-based case studies will evaluate its effectiveness in improving system manipulation in uncertain and dynamic environments, such as optimising energy storage systems under fluctuating demand and stabilising financial markets amid stochastic variations. My three objectives to be met over a 12-month period are as follows: Establish the theoretical underpinnings of the unified continuous-time probabilistic control framework. Design computational tools and validate my framework. Develop a long-term roadmap for the advancement of my proposed framework. While this research is primarily theoretical, its outcomes will pave the way for advanced monitoring, forecasting, and adaptive system manipulation in uncertain environments. Academically, this work will advance ongoing research in stochastic modelling, Bayesian inference, and optimal transport, establishing pathways for future applications and fostering collaborations with researchers and industry stakeholders. In the longer term, the framework has the potential to impact areas requiring uncertainty-aware decision-making, such as risk-sensitive control in engineering and data-driven system optimisation. Achievement of these objectives will lay the groundwork for a broader research programme, pursued through more comprehensive funding, such as an EPSRC standard grant.
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