Modeling of the Trajectory Optimization Problems

This chapter presents the general formulation of the trajectory optimization problems. To describe the multi-phase SMV skip entry problem, a new nonlinear constrained optimal control model is established. The constructed formulation contains multiple exo-atmospheric and atmospheric flight phases and correspondingly, two sets of flight dynamics. In addition, in order to guide the SMV overflying different target altitude points, a series of event sequences is constructed and embedded in the proposed formulation. A couple of interior-point constraints are also introduced so as to enhance the continuity of the trajectory between different flight phases. Following the construction of the optimal control model, a multi-phase global collocation technique is applied to discretize the continuous-time system. Initial simulations and different case studies are carried out. The obtained results reveal that it is feasible to use the proposed multi-phase optimal control formulation for fulfilling the multi-phase SMV skip entry mission.