First-order necessary conditions for optimality reveal the Hamiltonian nature of optimal control problems. Regardless of the overwhelming awareness of this result, the implications that it entails have not been fully explored. We discuss how the symplectic structure of optimal control constrains the flow of sub-volumes in the phase space....
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May 2019 (v1)Journal articleUploaded on: December 4, 2022
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May 20, 2018 (v1)Conference paper
First-order necessary conditions for optimality reveal the Hamiltonian nature of optimal control problems. Regardless of the overwhelming awareness of this result, the implications that it entails have not been fully explored. We discuss how the symplectic structure of optimal control constrains the flow of sub-volumes in the phase space....
Uploaded on: December 4, 2022 -
2023 (v1)Journal article
Upcoming missions toward remote planetary moons will fly in chaotic dynamic environments that are significantly perturbed by the oblateness of the host planet. Such a dominant perturbation is often neglected when designing spacecraft trajectories in planetary moon systems. This paper introduces a new time-periodic set of equations of motion...
Uploaded on: February 22, 2023 -
May 2019 (v1)Journal article
First-order necessary conditions for optimality reveal the Hamiltonian nature of optimal control problems. Regardless of the overwhelming awareness of this result, the implications that it entails have not been fully explored. We discuss how the symplectic structure of optimal control constrains the flow of sub-volumes in the phase space....
Uploaded on: February 22, 2023 -
June 12, 2023 (v1)Publication
Many observation satellites are subject to attitude constrains arising from peculiar mission requirements or environmental conditions. These obstructions often constrain the direction of the thrust vector to remain within a cone. In this study, we investigate the local controllability of station-keeping maneuvers of satellites with low thrust...
Uploaded on: July 13, 2023 -
February 7, 2023 (v1)Conference paper
National audience
Uploaded on: March 25, 2023 -
January 15, 2023 (v1)Conference paper
An algorithm for the numerical solution of low-thrust Lambert's problem is proposed. After averaging the extremal flow of the optimal control Hamiltonian, a one-parameter family of solutions of a reduced-order two-point boundary value problems is achieved by means of a differential continuation scheme. Sensitivities of the shooting function are...
Uploaded on: April 14, 2023 -
July 18, 2022 (v1)Conference paper
Averaging is a valuable technique to gain understanding of the long-term evolution of dynamical systems characterized by slow dynamics and fast periodic or quasi-periodic dynamics. Averaging the extremal flow of optimal control problems with one fast variable is possible if a special treatment of the adjoint to this fast variable is carried...
Uploaded on: December 3, 2022 -
March 28, 2018 (v1)Conference paper
National audience
Uploaded on: December 4, 2022 -
April 24, 2019 (v1)Conference paper
An increasing interest in optimal low-thrust orbital transfers was triggered in the last decade by technological progress in electric propulsion and by the ambition of efficiently leveraging on orbital perturbations to enhance the maneuverability of small satellites. The assessment of a control sequence that is capable of steering a satellite...
Uploaded on: December 4, 2022 -
April 2022 (v1)Journal article
We derive a new analytical solution for the first-order, short-periodic perturbations due to planetary oblateness and systematically compare our results to the classical Brouwer–Lyddane transformation. Our approach is based on the Milankovitch vectorial elements and is free of all the mathematical singularities. Being a non-canonical set, our...
Uploaded on: February 22, 2023 -
February 24, 2019 (v1)Conference paper
Most cartographic stability maps advocated for use in the new passive debris removal ideology based on orbital resonances are obtained through crude averaging methods. This means that from an operational perspective, its not clear where in the osculating space one should actually target to place the satellite on a natural disposal trajectory....
Uploaded on: December 4, 2022 -
June 29, 2021 (v1)Conference paper
For a control system with one fast periodic variable, with a small parameter measuring the ratio between time derivatives of fast and slow variables, we consider the Hamiltonian equation resulting from applying Pontryagin maximum principle for the minimum time problem with fixed initial and final slow variables and free fast variable. One may...
Uploaded on: December 4, 2022 -
2024 (v1)Journal article
An algorithm for the second-order approximation of fixed-time, low-thrust orbital transfersand generation of Bacon plots is proposed. After averaging the extremal flow of the optimal-control Hamiltonian, a one-parameter family of solutions of a reduced-order, two-point boundary value problems is computed by means of a differential-continuation...
Uploaded on: January 13, 2024 -
2020 (v1)Journal article
International audience
Uploaded on: December 4, 2022 -
2023 (v1)Journal article
Trajectory design and station keeping of solar sails about a celestial body can be formulated as control problems with positivity constraints. Specifically, when re-emitted radiation is neglected and the sail is modeled as a flat surface, which are reasonable assumptions for control purposes, force generated by solar radiation pressure is...
Uploaded on: December 3, 2022 -
June 22, 2022 (v1)Conference paper
This talk will be about local controllability of a control affine system along a reference solution x(.), defined on [0,T], corresponding to zero control, in the case where the zero control is on the boundary of the set U that constrains the control. We present a sufficient condition for the reachable set in time T from x(0) (with U-valued...
Uploaded on: December 3, 2022 -
September 16, 2022 (v1)Publication
No description
Uploaded on: December 4, 2022 -
January 11, 2018 (v1)Conference paper
We consider the minimum time control of dynamical systems with slow and fast state variables. With applications to perturbations of integrable systems in mind, we focus on the case of problems with one or more fast angles, together with a small drift on the slow part modelling a so-called secular evolution of the slow variables. According to...
Uploaded on: December 4, 2022 -
July 11, 2023 (v1)Publication
Optimal control of a solar sail orbiting around a fixed center of mass is considered. The sail is modelled as a plane surface with two sides having similar optical properties. The control is assumed to be the attitude of the sail and is so represented as an element of the projective plane. Mapping this plane to compute the actual force...
Uploaded on: July 14, 2023 -
October 1, 2018 (v1)Conference paper
The Martian Moons eXploration mission is currently under development at JAXA and will be the first spacecraft mission to retrieve pristine samples from the surface of Phobos. In preparation for the sampling operations, MMX will collect observations of Phobos from stable retrograde relative trajectories also known as quasi-satellite orbits or...
Uploaded on: December 4, 2022 -
2023 (v1)Publication
Optimal control of a solar sail orbiting around a fixed center of mass is considered. The sail is modelled as a plane surface with two sides having similar optical prop- erties. The control is assumed to be the attitude of the sail and is so represented as an element of the projective plane. Mapping this plane to compute the actual force...
Uploaded on: December 7, 2023 -
December 2022 (v1)Publication
Sufficient conditions are established for controllability of affine control systems with a drift all of whose solutions are periodic. In contrast with previously known results, these conditions encompass the case of a control set whose convex hull is not a neighbourhood of the origin. The condition is expressed by means of pushforwards along...
Uploaded on: December 7, 2023 -
March 2024 (v1)Publication
Sufficient and necessary conditions are established for controllability of affine control systems, motivated by these with a drift all of whose solutions are periodic.In contrast with previously known results, these conditions encompass the case of a control set whose convex hull contains the origin but is not a neighborhood of the origin.The...
Uploaded on: March 10, 2024 -
July 12, 2024 (v1)Journal article
Optimal control of a solar sail orbiting around a fixed center of mass is considered. The sail is modelled as a plane surface with two sides having similar optical properties. The control is assumed to be the attitude of the sail and is represented as an element of the projective plane. Mapping this plane into the three dimensional ambient...
Uploaded on: September 4, 2024