An Approach to Evaluate the Region of Attraction of Satellites Controlled by SDRE

Abstract

The control of a satellite can be designed with success by linear control theory if the satellite has slow angular motions. However, for fast maneuvers, the linearized models are not able to represent the effects of the nonlinear terms. One candidate technique for the design of the satellite’s control under fast maneuvers is the State- Dependent Riccati Equation (SDRE). SDRE provides an effective algorithm for synthesizing nonlinear feedback control by allowing nonlinearities. Nonetheless, much criticism has been leveled against the SDRE because it does not provide assurance of global asymptotic stability. Additionally, there are situations in which global asymptotic stability cannot be achieved (e.g., systems with multiple equilibrium points). Therefore, especially in aerospace, estimating the region of attraction (ROA) is fundamental. The Brazilian National Institute for Space Research (INPE, in Portuguese) was demanded by the Brazilian government to build remote-sensing satellites, such as the Amazonia-1 mission. In such missions, the satellite must be stabilized in three axes so that the optical payload can point to the desired target. In this paper, we share an approach to evaluate the ROAs of Amazonia-1 controlled by LQR (the linear counterpart of SDRE) and SDRE. The initial results showed SDRE has a larger ROA than LQR.