Title: Numerical methods for the optimal control of the heel angle of a rocket

Authors: Mohamed Aliane; Nacima Moussouni; Mohand Bentobache

Addresses: Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, Laghouat, 03000, Algeria ' Laboratory L2CSP, University of Tizi-Ouzou, Tizi-Ouzou, 15000, Algeria ' Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, Laghouat, 03000, Algeria

Abstract: In this work, we calculated the optimal heel angle trajectory of a rocket which have a constant mass and moves with a nonrectilinear motion from an initial point to a final one with a known altitude. The objective of the study is to maximise the lateral offset of the rocket. This problem is modelled as a nonlinear optimal control problem, where the control represents the heel angle of the rocket. In order to find a numerical solution to the problem, we applied the shooting method which is based on the Pontryagin's maximum principle, and the Euler discretisation method, then we developed an implementation with the MATLAB programming language. Finally, we presented simulation results which compare the two numerical methods.

Keywords: optimal control; heel angle of a rocket; Pontryagin's maximum principle; shooting method; Euler discretisation method; nonlinear programming.

DOI: 10.1504/IJMOR.2021.119975

International Journal of Mathematics in Operational Research, 2021 Vol.20 No.3, pp.418 - 431

Received: 25 Mar 2020
Accepted: 21 Aug 2020
Published online: 04 Jan 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article