| The primary purpose of this research is to investigate optimal trajectories and guidance of a launch vehicle for delivering large payloads into a low earth orbit. The necessary conditions for optimality and possible control switching structures have also been studied for optimal trajectories with a first-order state inequality constraint.; In the first part of the dissertation, the maximum final-mass trajectories for the model of a new generation of launch vehicles are presented. Two slightly different aerodynamic models, with different smoothness properties, cause appreciable differences in some state and control variables while the final time and the performance indices obtained are nearly the same. Although the hodographs are nonconvex along the optimal trajectories during certain time intervals, the optimal state rates remain on the convex domain and vary smoothly.; In the second part of the dissertation, implementation and results of a parallel shooting method for solving trajectory optimization problems on the nCUBE 6400 series parallel computer are discussed. Results of the increase in computational speed as a function of number of processors are presented.; In the third part of the dissertation, an alternate treatment of the necessary conditions for a touch point to occur in connection with a first-order state inequality constraint is presented. This study gives additional insights into the nature of the Lagrange multipliers at a touch point without solving the optimal control problem. The optimal trajectories in two dimensional flight show the touch point behavior, and satisfy the necessary conditions for optimality. The necessary conditions for existence of a touch point are not satisfied by the trajectories in three dimensional flight.; In the fourth part of this dissertation, a new guidance scheme is suggested to minimize the deviations from the nominal optimal trajectory due to perturbations. This approach uses the concept of the neighboring extremal path, determining the control variations as a linear function of the deviations. The new guidance scheme is applied to the ascent trajectories with errors in initial boundary conditions and model parameters. |
