Investigation of the Stability of Satellite Large Angle Attitude Manoeuvres Using Nonlinear Optimization Methods

Some theoretical investigations of large angle attitude manoeuvres have been based on the app l i ca ti on of Lyapunov' s stability theory. With this method r1ortensen derived stable control laws for performing attitude manoeuvres with either thrusters or reaction wheels. Previous results were idealized in that they i qnored the non l i neari ti es inherent in the opera ti on of both types of actuators. The present paper extends the scope of this work by acknowledging the actuator nonlinearities. The approach selected is to estimate the domain of attraction (DOA) of the target equilibrium for the system corresponding to the idealized control laws constrained by the actuator nonlinearities. The DOA is estimated by searching for the largest region of asymototic stability over a set of quadratic Lyapunov functions . This approach results from the apolication of a theorem of Lasalle and gives rise to two nested nonlinear optimization problems, the internal one of which is a constrained global problem with several local minima. The paoer gives an overview of the progress made in solving problems of this complexity. Emphasis has been placed on the parametrization of quadratic Lyapunov functions and a detailed comparison of several candidate nonlinear ortimization techniques has been made for both the constrained and the unconstrained optimization problem. Areas requiring further research are identified . KeyUJOrds . Large anql e a tti tu de manoeuvres, Lyapunov stability theory, control actuator nonlinearities, nonlinear global optimization, nested optimization procedures.