Methodology for Satellite Formation-Keeping in the Presence of System Uncertainties

A two-step formation-keeping control methodology is proposed that includes both attitude and orbital control requirements in the presence of uncertainties. Based on a nominal systemmodel that provides the best assessment of the real-life uncertain environment, a nonlinear controller that satisfies the required attitude and orbital requirements is first developed. This controller allows the nonlinear nominal system to exactly track the desired attitude and orbital requirements without making any linearizations/approximations. In the second step, a new additional set of closed-form additive continuous controllers is developed. These continuous controllers compensate for uncertainties in the physical model of the satellite and in the forces to which it may be subjected. They obviate the problem of chattering. The desired trajectory of the nominal system is used as the tracking signal, and these controllers are based on a generalization of the concept of sliding surfaces. Error bounds on tracking due to the presence of uncertainties are analytically obtained. The resulting closed-form methodology permits the desired attitude and orbital requirements of the nominal system to be met within user-specified bounds in the presence of unknown, but bounded, uncertainties. Numerical results are provided, showing the simplicity and efficacy of the control methodology, and the reliability of the analytically obtained error bounds.