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Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach

Khurshudyan A. Zh.

Archives of Control Sciences

2018

Vol. 28, No. 3

335--347

We study the exact and approximate controllabilities of the Langevin equation describing the Brownian motion of particles with a white noise. The Langevin equation is shown to describe also the bacterial run-and-tumble motion. Applying the Green’s function approach to the Green’s function representation of the Langevin equation, we obtain necessary and sufficient conditions for exact controllability in the form of a finite-dimensional problem of moments. For the approximate controllability, we obtain only sufficient conditions. The sets of resolving controls are characterized in both cases. The theoretical derivations are supported by a numerical analysis.