Satellite attitude control using statistical game theory

We consider the application of multi-objective statistical game theory to a remote sensing satellite attitude control. Statistical game theory is a generalization of mixed H
₂
/H
_infin
control, where we have two objective functions and we optimize the higher order cumulants of these objective functions. We use previously developed satellite attitude model with thrusters, gravity torquers and a reaction wheel cluster. Then we control the satellite attitude using the statistical game (Minimal Cost Variance/H
_infin
) control, H
_infin
control, and mixed H
₂
/H
_infin
control. Throughout the simulations, statistical game control has an extra degree of freedom to improve the performance and reduce the overshoot and undershoot compared to either H
_infin
control and H
₂
/H
_infin
control. The simulations show that the performance of Minimal Cost Variance/H
_infin
is 8.8% and 5.4% faster than H
₂
/H
_infin
and H
_infin
control, respectively. Moreover, the control actions of MCV/H
_infin
is reduced by 67% compared to H
_infin
control and 55% compared to H
₂
/H
_infin
control. So, we achieve both performance improvement while saving the control energy. In the case of the stability margin, MCV/H
_infin
control has the highest stability margin, H
_infin
control has the lowest, and H
₂
/H
_infin
control an intermediate value between those two.