Orbit Transfer using Optimal Control Theory

Main objective for the orbit transfer problem is optimal minimization of time and fuel. In this research, 2-body system is represented by a nonlinear dynamic system. Theoretical analysis of Euler-Lagrange and Hamiltonian function is implemented for the application of optimal control. Certain assumptions are taken into account such as continuous thrust acceleration for the entire interval, unbounded control variables, and presence of certain state variables designated at terminal boundary conditions. These provide solution for the orbital transfer between 7000 km circular orbit and 8000 km circular orbit, which are coplanar in nature, by uniting a Linear Quadratic Regulator (LQR) and the Shooting method. For determining indirect optimal results about fuel or time, obtained results are compared with the Hohmann transfer. It is observed through the numerical simulations that the optimal theory applied coplanar rendezvous maneuver is optimally comparable to the minimum energy solution.