Geometric aspects of force controllability for a swimming model

Applied Mathematics and Optimization

Volumn 57, Issue 1, 2008, Pages 98-124

  Khapalov, A Y ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Controllability; Coupled systems; Multiplicative control; Stokes equation; Swimming model

Indexed keywords

COUPLED SYSTEMS; SWIMMING MODELS;

BIOLOGY; COMPUTATIONAL GEOMETRY; MATHEMATICAL MODELS; PROBLEM SOLVING;

FORCE CONTROL;

EID: 38849189968     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-007-9013-x     Document Type: Article

References (19)

1. Ball, J.M., Mardsen, J.E., Slemrod, M.: Controllability for distributed bilinear systems. SIAM J. Control Opt. 20, 575-597 (1982)
2. Childress, S.: Mechanics of Swimming and Flying. Cambridge University Press, Cambridge (1981)
3. Fauci, L.J.: Computational modeling of the swimming of biflagellated algal cells. Contemp. Math. 141, 91-102 (1993)
4. Fauci, L.J., Peskin, C.S.: A computational model of aquatic animal locomotion. J. Comp. Phys. 77, 85-108 (1988)
5. Hirose, S.: Biologically Inspired Robots: Snake-like Locomotors and Manipulators. Oxford University Press, Oxford (1993)
6. Khapalov, A.Y.: Bilinear control for global controllability of the semilinear parabolic equations with superlinear terms, the Special volume "Control of Nonlinear Distributed Parameter Systems," dedicated to D. Russell, G. Chen, I. Lasiecka, J. Zhou (eds.) pp. 139-155. Dekker (2001)
7. Khapalov, A.Y.: Global non-negative controllability of the semilinear parabolic equation governed by bilinear control. ESAIM: Contrôl. Optim. Calc. Var. 7, 269-283 (2002)
8. Khapalov, A.Y.: Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: a qualitative approach. SIAM J. Control Optim. 41, 1886-1900 (2003)
9. Khapalov, A.Y.: Controllability properties of a vibrating string with variable axial load. Discret. Cont. Dyn. Syst. 11, 311-324 (2004)
10. Khapalov, A.Y.: The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, preprint. Available as Techn. Rep. 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5. pdf
11. Khapalov, A.Y.: Local controllability for a "swimming" model. SIAM J. Control Opt. 46, 655-682 (2007)
12. Ladyzhenskaya, O.H.: The Mathematical Theory of Viscous Incompressible Flow. Cordon and Breach, New York (1963)
13. Lighthill, M.J.: Mathematics of Biofluiddynamics. Society for Industrial and Applied Mathematics, Philadelphia (1975)
14. McIsaac, K.A., Ostrowski, J.P.: Motion planning for dynamic eel-like robots. In Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, pp. 1695-1700 (2000)
15. Martinez, S., Cortés, J.: Geometric control of robotic locomotion systems, In Proc. X Fall Workshop on Geometry and Physics, Madrid, 2001, Publ. de la RSME, vol. 4, pp. 183-198 (2001)
16. Peskin, C.S.: Numerical analysis of blood flow in the heart. J. Comp. Phys. 25, 220-252 (1977)
17. Peskin, C.S., McQueen, D.M.: A general method for the computer simulation of biological systems interacting with fluids. SEB Symposium on biological fluid dynamics, Leeds, England, 5-8 July 1994
18. Symon, K.R.: Mechanics. Addison-Wesley, Reading (1971)
19. Temam, R.: Navier-Stokes Equations. North-Holland, Amsterdam (1984)