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

• Autorzy: Khurshudyan A. Zh.

Identyfikatory

DOI

10.24425/acs.2018.124706

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

run; tumble; micro-swimmers; Green’s function of nonlinear equation; discontinuous

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2018
• Tom: Vol. 28, No. 3
• Strony: 335--347
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr., wzory

Twórcy

autor

Khurshudyan A. Zh.

• Department of Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, NAS of Armenia, 24B Baghramyan ave., 0019, Yerevan, Armenia
• Institute of Natural Sciences, Shanghai Jiao Tong University, 800 Dong Chuan rd., 200240, Shanghai, P. R. China

Bibliografia

• [1] S. Sundararajan, P. E. Lammert and A. W. Zudans: Catalytic motors for transport of colloidal cargo, Nano Lett., 8 (2008), 1271-1276.
• [2] A. M. Fennimore, et al.: Rotational actuators based on carbon nanotubes, Nature, 424, 408-410.
• [3] M. Eisenbach: Chemotaxis, Imperial College Press, London (2004).
• [4] T. Mano, J.-B. Delfau, J. Iwasawa and M. Sano: Optimal run-and-tumble based transportation of a Janus particle with active steering, PNAS, 114 (2017), E2580–E2589.
• [5] G. Fier, D. Hansmann And R. C. Buceta: A stochastic model for directional changes of swimming bacteria, Soft Matter, 13 (2017), 3385–3394.
• [6] G. Fier, D. Hansmann and R. C. Buceta: Langevin equations for the run-and-tumble of swimming bacteria, ArXiv:1802.00269v1.
• [7] M. Lefebvre: Optimal and suboptimal control of a standard brownian motion, Archives of Control Sciences, Vol. 26(3) (2016), 383–394.
• [8] A. S. Avetisyan and As. Zh. Khurshudyan: Controllability of Dynamic Systems. The Green’s Function Approach, Cambridge Scholars, Cambridge, 2018.
• [9] As. Zh. Khurshudyan: Heuristic determination of Resolving controls for exact and approximate controllability of nonlinear dynamic systems, Mathematical Problems In Engineering (2018), Article ID 9496371, 16 pages.

Uwagi

EN

1. I wish to express my sincere gratitude to Prof. Hepeng Zhang (Shanghai Jiao Tong University) for bringing the problem to my attention and to Prof. Min Tang (Shanghai Jiao Tong University) for helpful discussions.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).