# American Institute of Mathematical Sciences

January  2008, 20(1): 1-35. doi: 10.3934/dcds.2008.20.1

## Impulsive control of Lagrangian systems and locomotion in fluids

 1 Department of Mathematics, Penn State University, University Park, Pa.16802

Received  September 2006 Revised  July 2007 Published  October 2007

Aim of this paper is to provide a survey of the theory of impulsive control of Lagrangian systems. It is assumed here that an external controller can determine the evolution of the system by directly prescribing the values of some of the coordinates. We begin by motivating the theory with a couple of elementary examples. Then we discuss the analytical form taken by the equations of motion, and their impulsive character. The following sections review various results found in the literature concerning the continuity of the control-to-trajectory map, the existence of optimal controls, and the asymptotic controllability to a reference state. In the last section we indicate a further application of the theory, to the control of deformable bodies immersed in a fluid.
Citation: Alberto Bressan. Impulsive control of Lagrangian systems and locomotion in fluids. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 1-35. doi: 10.3934/dcds.2008.20.1
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