Advanced control strategies for stochastic systems using PDF optimisation

Warwick Mathematics Institute, Warwick University, Coventry CV4 7AL, UK

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 13 February 2025
Accepted: 20 November 2025

Abstract

This paper presents an innovative probabilistic control framework for continuous-time stochastic systems. Unlike traditional control approaches that optimise deterministic control strategies, our framework directly optimises the probability density function (PDF) of the control signal, allowing for a more adaptable and robust response to stochastic variations. By integrating stochastic differential equations with the Hamilton–Jacobi–Bellman equation and utilising the Fokker–Planck dynamics, our method offers a precise and dynamic approach to managing uncertainty. The framework minimises the Kullback–Leibler divergence to align the system’s joint state and control distribution with a desired joint target distribution, ensuring effective control even in unpredictable environments. A novel algorithm iteratively refines the control PDF based on real-time feedback, further enhancing the system’s alignment with the target behaviour. The proposed method is demonstrated on an Ornstein–Uhlenbeck process, showcasing its effectiveness in steering the system’s state distribution toward desired outcomes and underscoring its broad applicability to stochastic systems.