5. Adaptive Dynamic Inversion for Satellite Formation Flying

The benefit of satellite formation flying can truly be realized with greater mission flexibility such as higher inter-satellite separation, formation in elliptic orbits, etc. However, under the above-enhanced conditions, linear system dynamics based control design approaches fail to achieve the desired objectives. Even though the LQR philosophy inspired the SDRE approach discussed in Chapter 3 offers a limited solution, it suffers from the drawback that the success of the approach largely depends on the typical state-dependent coefficient form one adopts (which remains as ‘art’). Moreover, if the eccentricity deviates significantly from circular orbit or separation distance requirement becomes large significantly, even SDRE can fail. The Adaptive LQR offers a fairly good solution to this issue, but introduces neural network learning concepts even for the system dynamics that is fairly known which can be handled directly. This brings in additional transients at the beginning of learning as well, which should preferably be avoided. In view of these observations, this chapter presents an alternate approach that need not be optimal, but can be successful under such realistic conditions as well.