Alesia Herasimenka soutient sa thèse intitulée « Contrôle optimal des voiles solaires » le jeudi 7 septembre 2023 à 14:00, amphi Forum de Polytech Nice Sophia, devant le jury composé de :
- Bernd Dachwald (Aachen University, rapporteur)
- Daniel J. Scheeres (University of Colorado, rapporteur)
- Emmanuel Trélat (Sorbonne Université, rapporteur)
- Ariadna Farrès (NASA, examinatrice)
- Pascal Morin (Sorbonne Université, examinateur)
- Massimo Casasco (ESA, invité)
- Jean-Baptiste Caillau (UCA, co-directeur)
- Lamberto Dell’Elce (Inria UCA, co-directeur)
- Jean-Baptiste Pomet (Inria UCA, co-encadrant)
Optimal control of solar sails
This thesis focuses on the optimal control of solar sails, which are spacecraft propelled by solar radiation pressure. Solar sails generate propulsive force by reflecting and absorbing photons, making them a cost-effective and practically unlimited means of space propulsion. The first part of this thesis is dedicated to the controllability study of solar sails. The primary challenge in assessing their controllability arises from the specific constraints imposed on the control set. Due to the nature of solar radiation pressure, a solar sail can only generate force whose directions belong to a convex cone, and is unable to create a force directed towards the Sun. Traditional methods for evaluating controllability are inadequate due to these specific constraints. To address this challenge, an alternative condition is proposed, which involves identifying forbidden directions in the tangent bundle associated with the system state manifold. These theoretical results are applicable to any periodic system with a conical constraint on its control set. To verify this condition, a convex optimization problem is formulated, enabling an effective assessment. The solution utilizes the theory of squared functional systems and the ability to express the dynamics by means of trigonometric polynomials. A significant contribution of this study is the determination of a minimum requirement in terms of optical properties that satisfy the necessary local controllability condition. This minimum angle provides valuable insights into the optical constraints of solar sails, facilitating their design for space missions. Furthermore, this methodology is expanded so as to be applicable to any periodic orbit and any type of propulsion for station-keeping purposes. The second contribution of this thesis is an algorithm designed to compute the optimal control inputs for steering the sail towards a desired direction within the phase space. The algorithm employs convex optimization to obtain an admissible yet suboptimal control as an initial input. Subsequently, an optimal control problem is solved to maximize the displacement in the desired direction. By analyzing the Hamiltonian dynamics of the system, the relevant switching function that governs the structure of the solution is identified. Additionally, an upper bound on the number of zeros of this function is established, enabling the efficient implementation of a multiple shooting code using differential continuation. Finally, an original scenario of a Sun occultation mission is analyzed using optimal control techniques. The Earth is used to occult the Sun, so that Solar corona can be observed. A solar sail is used to carry out periodic observations by repeatedly steering the satellite inside and outside of the observation zone.
