4. Adaptive LQR for Satellite Formation Flying

As shown in Chapter 3, a linearized relative dynamics based LQR control theory does not lead to satisfactory results when the formation is desired in an elliptic orbit and/or when the relative separation is high. It was also demonstrated in Chapter 6 that the SDRE approach is a relatively better to address such issues to a reasonable extent. Unfortunately, however, practicing engineers are typically not comfortable to switch over to nonlinear control theory completely. In view of this, an alternate approach is presented here. This approach uses the standard infinite-time LQR control as the nominal controller. However, it is augmented with online learning based adaptive optimal controller that accounts for the effects of the neglected system dynamics and external state-dependent disturbances together. This additional adaptive component in fact is computed from the identified system. The overall controller is termed as ‘Adaptive LQR’ controller for obvious reasons. As expected, this Adaptive LQR controller performs much better than the nominal LQR controller. It is worth mentioning here that this technique is capable enough to handle small eccentricity as well as large desired relative distance scenarios. Details of the process are discussed next.