Launch ascent guidance by discrete multi-model predictive control

This paper studies the application of discrete multi-model predictive control as a trajectory tracking guidance law for a space launcher. Two different algorithms are developed, each one based on a different representation of launcher translation dynamics. These representations are based on an interpolation of the linear approximation of nonlinear pseudo-five degrees of freedom equations of translation around an elliptical Earth. The interpolation gives a linear-time-varying representation and a linear-fractional representation. They are used as the predictive model of multi-model predictive controllers. The controlled variables are the orbital parameters, and constraints on a terminal region for the minimal accepted precision are also included. Use of orbital parameters as the controlled variables allows for a partial definition of the trajectory. Constraints can also be included in multi-model predictive control to reduce the number of unknowns of the problem by defining input shaping constraints. The guidance algorithms are tested in nominal conditions and off-nominal conditions with uncertainties on the thrust. The results are compared to those of a similar formulation with a nonlinear model predictive controller and to a guidance method based on the resolution of a simplified version of the two-point boundary value problem. In nominal conditions, the model predictive controllers are more precise and produce a more optimal trajectory but are longer to compute than the two-point boundary solution. Moreover, in presence of uncertainties, developed algorithms exhibit poor robustness properties. The multi-model predictive control algorithms do not reach the desired orbit while the nonlinear model predictive control algorithm still converges but produces larger maneuvers than the other method. (C) 2013 IAA. Published by Elsevier Ltd. All rights reserved.