Interval Uncertainty-Oriented Optimal Control Method for Spacecraft Attitude Control

Abstract

Research on uncertainty-oriented optimal attitude control of spacecraft with complex space environments and multi-source uncertainties is a research hotspot. Considering that the uncertain parameters in the control system are difficult to quantify, this study proposed an interval uncertainty-oriented optimal control method based on the linear quadratic regulator (LQR) for spacecraft attitude control. The interval state-space equation of the spacecraft attitude dynamic with uncertain controlled feedback gain was constituted by expanding the deterministic model into an order-extended interval matrix format. Based on the interval uncertainty propagation method, the interval-based Riccati equation in LQR was proposed using the modified interval estimation method. Therefore, the interval-controlled feedback gain and interval cost function could be obtained, and the overestimation attributed to the interval expansion could be avoided. The interval-based reliability was investigated using the state-threshold interference model, and the interval-based safety index was developed. The interval uncertainty-based multi-objective optimal control model with constraints was proposed to balance both minimizations of the optimal control cost function and state vector fluctuation by considering these two interval indices as the constraints in optimal control. A flowchart and a numerical example of satellite attitude control were applied to reflect the effectiveness.