Advanced control strategies for stochastic systems using PDF optimisation

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.