# Analytical Initialization of a Continuation-Based Indirect Method for Optimal Control of Endo-Atmospheric Launch Vehicle Systems

## TL;DR

This paper introduces an analytical initialization strategy for indirect optimal control methods applied to endo-atmospheric launch vehicles, combining simplified analytical guidance with continuation techniques to improve convergence.

## Contribution

It presents a novel approach that integrates analytical solutions and continuation algorithms to enhance indirect optimal control of launch vehicles.

## Key findings

- Successful convergence to optimal solutions demonstrated.
- Improved initial guess reduces computation time.
- Method applicable to complex launch vehicle dynamics.

## Abstract

In this paper, we propose a strategy to solve endo-atmospheric launch vehicle optimal control problems using indirect methods. More specifically, we combine shooting methods with an adequate continuation algorithm, taking advantage of the knowledge of an analytical solution of a simpler problem. This procedure is resumed in two main steps. We first simplify the physical dynamics to obtain an analytical guidance law which is used as initial guess for a shooting method. Then, a continuation procedure makes the problem converge to the complete dynamics leading to the optimal solution of the original system. Numerical results are presented.