Optimal control of a rectilinear motion of a rocket

  • Mohamed Aliane Laboratory of Pure and Applied Mathematics, LMPA, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000 Laghouat, Algeria;
  • Nacima Moussouni Laboratory L2CSP, University of Tizi-Ouzou, Algeria
  • Mohand Bentobache Laboratory of Pure and Applied Mathematics, LMPA, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000 Laghouat, Algeria;
Keywords: Optimal control, Pontryagin maximum principle, shooting method, Cauchy discretization method, Euler discretization method

Abstract

In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.

Author Biographies

Mohamed Aliane, Laboratory of Pure and Applied Mathematics, LMPA, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000 Laghouat, Algeria;
Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Algeria
Nacima Moussouni, Laboratory L2CSP, University of Tizi-Ouzou, Algeria
Laboratory L2CSP, University of Tizi-Ouzou, 15000, Tizi-Ouzou, Algeria;
Mohand Bentobache, Laboratory of Pure and Applied Mathematics, LMPA, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000 Laghouat, Algeria;
Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Algeria

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Published
2020-02-18
How to Cite
Aliane, M., Moussouni, N., & Bentobache, M. (2020). Optimal control of a rectilinear motion of a rocket. Statistics, Optimization & Information Computing, 8(1), 281-295. https://doi.org/10.19139/soic-2310-5070-741
Section
Research Articles