Dynamic programming based approach for optimal transport by flashing ratchet against a load force

Flashing ratchet is a mechanism which employs noise under isothermal and non equilibrium conditions. Its primary is to transport of small particles, possibly against a load force, under the influence of thermal noise and potential energy landscapes that can be realized locally, near the particles position. In this article we present a dynamic programming based approach to analyze and synthesize optimal strategies in the presence of a non-zero load force and finite sampling intervals. We show that it is possible to obtain an order increase in velocity and stalling force, over open-loop strategies. Besides engineered systems, study of such strategy is also important to gain insights on the intra-cellular transport of motor proteins (such as Kinesin and Dynein) on a microtubular track, and on the role of feedback control on their transport.