Optimal Control Procedure for Calculating a Typical Lunch Vehicle Trajectory Based on Maximizing Payload

In this research optimal trajectory of lunch vehicle based on maximizing payload is being attended. At first, motion of missile concluding modeling of environment, atmosphere, gravity, mass, motion equations and aerodynamic coefficients would be simulated. Then procedure of an optimized design by using optimal control theory would be described. Applying variational calculus and mathematical modeling of optimization problems would lead project to a two point boundary condition problem which would be solved by numerical solutions such as steepest descent. At last a code would be generated in which optimal trajectory of missile calculated by using indirect optimal control and steepest descent numerical solution. An interesting point in this article is that some variables are used both as state and control variables. Hence state control variables here are divided to two groups, slow state variables concluding ones which are only state variables, and fast state variables concluding ones which are both state variables and control variables simultaneously. Solution for such control problems is described here.