Robust Stabilization of Uncertain, Unstable Periodic Orbits Using Generalized Sampled-data Hold Function Control

The problem of robust stabilization of unstable periodic solutions of nonlinear dynamic systems subject to parametric uncertainties is treated. The challenge is to achieve robust stability of orbital motion when both the period and the location of the periodic orbit are uncertain. The technical approach used here is to extend the method of Generalized Sampled-data Hold Function control of linear periodic systems in two ways. First, a change of independent variable is introduced, from time to a new angular variable, making the control logic eventdriven rather than time-driven. Second, an adaptation strategy is introduced, whereby the uncertain parameters are estimated online, the reference periodic orbit is computed based on the parameter estimates, and event-driven control is implemented to stabilize the motion about the parameter-dependent reference periodic orbit. The robustness of this adaptive event-driven strategy is illustrated by the robust stabilization of an unstable Halo orbit in a general planet-satellite system under uncertainty of the mass parameter. AAS 05-283