Dynamics and control of the system of a 2-D rigid circular cylinder and point vortices

The Hamiltonian system of a 2-D rigid circular cylinder dynamically interacting with N point vortices in its vicinity [16] is an idealized example of coupled solid-fluid systems interacting in the presence of vorticity and has applications to problems in engineering, such as locomotion of autonomous underwater vehicles, and in nature, such as swimming of fish. The first half of the paper presents simulation results and analysis of the system with N = 1 and N = 2, where the latter case is more relevant to the swimming of fish. The second half of this paper is devoted to theoretical analysis of the timeoptimal control of the system. The control input is a bounded external force acting through the cylinder center-of-mass. The Maximum Principle and its later extensions, in particular those due to Sontag and Sussmann, are applied to this system for the case of the cylinder interacting with a single point vortex to arrive at conclusions regarding characteristics of the timeoptimal controller.