Iterative control strategies for non-linear systems

TL;DR

This paper develops iterative control strategies for non-linear Langevin systems, deriving a universal control formula for displacing mean field equilibria, with potential applications in optimal work extraction.

Contribution

It introduces a novel iterative linear approximation method to control non-linear Langevin networks and reveals a universal form of the control function under specific conditions.

Findings

Derived a control formula for non-linear Langevin systems

Identified a universal control function form under certain conditions

Discussed applications in optimal work extraction

Abstract

In this paper, we focus on the control of the mean field equilibrium of non linear networks of the Langevin type in the limit of small noise. Using iterative linear approximations, we derive a formula that prescribes a control strategy in order to displace the equilibrium state of a given system, and remarkably find that the control function has a "universal" form under certain physical conditions. This result can be employed to define universal protocols useful, for example, in the optimal work extraction from a given reservoir. Generalizations and limits of application of the method are discussed.