GEOMETRIC CONSTRUCTION OF PERIODIC TRAJECTORIES

In this paper a method for generating periodic trajectories to a class of Hamiltonian systems is presented. A periodic Hamiltonian system will be defined as the target equilibrium for systems in strict feedback form. Parameter dependent nonlinear oscillation is introduced in a two dimensional subsystem and extended to higher dimensions using backstepping. A parameter update law which guarantees that the system converges to the optimal periodic orbit with respect to a given parametrization is then used for on-line implementation. A simple control problem is used to illustrate the application of this approach.