Comparative analysis of autonomous control methods for small spacecraft

Abstract

A specialized methodology was developed, computer modeling was conducted, and a comparative analysis was performed for autonomous control methods for small spacecraft, differing in how the nonlinearity of the initial stabilization problem is taken into account: — control constructed using a system of linear differential equations (SLDE); — control constructed using SLDE applied to a more general system of differential equations in which nonlinear terms are taken into account in trajectory calculations; — control using the SDRE method for a nonlinear system of differential equations. To evaluate the effectiveness of the three control methods under consideration under identical initial conditions, stabilization problems using the quadratic quality criterion (LQR) were considered. A computational experiment showed that, in most cases, the SDRE method yields the lowest quality functional of the three control methods considered. However, the final quality functional values for control constructed using SLDE with nonlinear terms remain consistently higher than those for SDRE. This is due to the fact that the nonlinear term significantly contributes to the increase in the quality functional in the initial equations. Unlike linear optimal control, the SDRE method used does not provide the necessary condition for a minimum performance functional, but it does not require the linearity of the initial differential equation system, which is a significant advantage. Despite the lack of a mathematical proof of the minimal performance functional for all cases, numerical experiments nevertheless demonstrate the advantages of the SDRE method for calculating control. However, the lack of a proven minimum performance functional allows this method to be considered a suboptimal control method. The described approach, using a mathematical model of suboptimal control for small spacecraft, allows it to be used to solve energy-intensive problems that largely determine the operational life of such spacecraft