Minimum Information Variability in Linear Langevin Systems Via Model Predictive Control

Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. If successful, this will benefit a wide range of practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a method of control based on the model predictive control technique and the information geometric theory applied to linear Langevin systems. Specifically, we combine an online optimisation method and the concept of information length to minimise the deviations from the geodesic of the system’s probability distribution through time. In addition, we analyse the effects on the closedloop system’s entropy production and entropy rate. The methodology is tested numerically in the Ornstein–Uhlenbeck process and the Kramers equation to illustrate its feasibility.