Near optimal trajectory generation of an ascent phase launch vehicle with minimum control effort

The offline trajectory optimization is carried out for a single stage of a multi stage launch vehicle. The problem is solved using classical steepest descent method by considering the control parameter to be the angle of attack. The behavior of the system is studied, with and without minimum control including constraints. The process has been carried out, starting from mathematical formulation to the offline trajectory generation. The formulation entails nonlinear 2- dimensional launch vehicle flight dynamics with mixed boundary conditions and multiple constraints. The objective is to reduce the terminal error. The problem is stated as a fixed time boundary problem, since the burn duration of the liquid propellant engine is fixed. Numerical results are analyzed with effectiveness of the minimum control problem, and the optimal flight procedure and trajectory were obtained.