Stability Analysis and RBF Neural Network Control of Second-Order Nonlinear Satellite System

This article studies the open-loop stability analysis and radial-basis-function-based neural network (RBFNN) control of triangular tethered satellite formation (TTSF) systems, comprised of the in-plane and out-plane dynamics. The dynamical equations of TTSF are nonlinear coupled second-order differential equations (DEs), whose explicit solutions are hard to work out. Therefore, the dynamics of systems are analyzed by imposing some constraints on initial states, and the norms of proper initialization for such TTSF systems are obtained by solving the DE. As a result, the nonlinear controllers achieving stable tracking to reference states of TTSF systems are designed based on open-loop analysis. Furthermore, when the structure information of the system is uncertain, delay-sampled neural network and offline training neural network control algorithms are proposed to train the RBFNN, and the optimal weights of the neural network are computed by the least squares method. Then, RBFNN control is imposed to the uncertain TTSF system to ensure stable tracking, and the stability proof of the control is given. Finally, simulations are taken on the specific motions of the TTSF system to test the theoretical results.