The quest for controlControlled molecular manipulation means knowing the transient conformations and positions of the molecule during manipulation and using this information to reach in a controlled way a target state.
As soon as the relation molecular conformation <----> measurement value has been mapped out completely by automated experiments and machine learning, the identification of precise molecular conformations at any time during manipulation becomes possible. The manipulation process can be described as a hidden Markov chain of incremental tip displacement steps that move the tip through a trajectory Rtip,1,…, Rtip,J, where 1 … J enumerate the discrete steps. We will therefore infer the (hidden) conformations during manipulation from the measured sequence of Δf values [Δf (Rtip,1)…Δf (Rtip,J)] and the manipulation map by employing a particle filter, a method that is used in control theory. In this method a cloud of particles is generated in tip position space of the manipulation map. The particles are randomly distributed around the estimated initial state of the junction (right after tip-molecule contact) and propagated in the manipulation map with each tip displacement step. After J tip steps each particle is characterized by a unique trajectory and sequence [Δf (Rtip,1)…Δf (Rtip,J)] of Δf values read off from the manipulation map. Of these, the actual tip trajectory in the experiment is the one whose sequence matches best with the measured sequence. To avoid unraveling, we will in certain intervals re-condense the cloud of particles around the region of highest probability.
R. Findeisen et al. Control on a molecular scale: A perspective, American Control Conference (ACC) (2016)
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