TY - JOUR N2 - 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. L1 - http://journals.pan.pl/Content/108825/PDF/ACS-2018-3-1.pdf L2 - http://journals.pan.pl/Content/108825 PY - 2018 IS - No 3 EP - 335–347 DO - 10.24425/acs.2018.124706 KW - run KW - tumble KW - micro-swimmers KW - Green’s function of nonlinear equation KW - discontinuous control A1 - Khurshudyan, Asatur Zh. PB - Committee of Automatic Control and Robotics PAS VL - vol. 28 DA - 2018.10.01 T1 - Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach SP - 335–347 UR - http://journals.pan.pl/dlibra/publication/edition/108825 T2 - Archives of Control Sciences ER -