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 H₂/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 H₂/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 H₂/H_infin control. The simulations show that the performance of Minimal Cost Variance/H_infin is 8.8% and 5.4% faster than H₂/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 H₂/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 H₂/H_infin control an intermediate value between those two.