Investigating the effect of hybrid objective function on robust and reliable optimization for spacecraft attitude control problem

In this paper, the attitude control problem of a spacecraft is investigated from the perspective of robust and reliable non-deterministic optimization with the assumption of parametric uncertainty in terms of a combined objective function. The attitude angles of a rigid spacecraft are controlled with a two-state on-off range share, a pulse width and frequency integrator, and an extended proportional-integral-derivative controller. In order to reduce the computational burden and achieve results with a wider application range, the spacecraft's state equations are extracted in a quasi-dimensional form. Uncertainty on the spacecraft's moment of inertia parameters, the amplitude of external disturbances, and the integrator model are considered as the standard deviation of the uncertainty percentage. A robust optimization approach is considered to achieve minimal changes in the objective function with the assumption of parametric uncertainty, and a reliable optimization approach is selected to achieve minimal violations of the problem's constraints with the assumption of parametric uncertainty. In this study, achieving the two optimization objectives mentioned above is investigated simultaneously, and in some cases, a compromise is made between the two with the weight coefficient of the combined objective function. The results show that in the robust optimization approach, the state error rate in the face of uncertainty is lower, and in the reliability optimization approach, the reliability rate is higher. In addition, depending on the weight coefficient of the combined objective function, a compromise between the reliability rate and the robustness of the state control can be selected.