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Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum "geometric information variability". We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control. [ABSTRACT FROM AUTHOR]

Distributed model predictive control is a wide-spread control method for systems such as mobile robots or vehicles, which operate in a shared space. Each system computes in an iterative way its control actions by locally solving an optimal control problem with regards to an objective function and subject to constraints arising from the system itself and from shared and possibly quantised information. Within state-of-the-art methods, local problems are solved sequentially and applied in a fixed order, which may not be optimal considering the overall system performance. We introduce dynamic priority rules, which are evaluated locally to establish a dynamic sequence of systems in each time instant. To avoid deadlocks possibly arising from periodic reordering, the idea is complemented by a memory rule. The impact of the proposed methods with and without quantisation is analysed via numerical simulations, revealing shorter convergence times in comparison to the state-of-the art approach. [ABSTRACT FROM AUTHOR]