Optimal Control of Mission Design in Multi-Body Models

Abstract

This dissertation contributes three general steps of space transfer problem. As the first step, this problem is mathematically modelled. Fortunately, it is not an untouched problem, and has been one of the most well-known and challenging problems in mathematics, physics and engineering. Actually, it is known as the Multi-Body System, since 18th century till now. During the first step, lots of transfer problem's elements have to be determined. The position, velocity and timing of the start maneuver, the restrictions on position and velocity in the space, especially in the vicinity of the Earth, limits on facilities, etc. are crucial in the mathematical modeling. On the other hand, since the main problem is an interplanetary problem, thus the determination of the final condition is also very important to be exactly understood and obtained. The second step of the space transfer problem is analysis the mathematical model achieved in the first step. It will be discussed that the system is classified as a chaotic system. After analyzing the behaviour of the system, we would like to control its chaotic behaviour such that some favourite goals are successfully achieved. This step of the study is namely the control of the system. To this end, a new approach is selected which model the transfer problem as an optimal control problem. There are a lot of methods to solve an optimal control problem. Among different classes of solution methods, the direct method is selected which has its own advantages and disadvantages. Its most important advantage is the ability of using the well developed theory of nonlinear programming problem which has been investigated for many decades. The direct method discretizes the transfer optimal control problem and transcribes it into a nonlinear programming problem. Solving the nonlinear programming problem leads to the optimal solutions, i.e. the optimal trajectory and control. After achieving the optimal solutions, the presented method uses the parametric sensitivity analysis of the discretized nonlinear programming problem and investigates the sensitivity of the optimal solutions with respect to the perturbations. At last, this method contributes a real-time control to correct the violations during the mission. The numerical results regarding an extensive collection of transfer examples show the applicability of the presented method.