0000000000671001
AUTHOR
Jean-baptiste Caillau
Convexity of injectivity domains on the ellipsoid of revolution: The oblate case (addendum)
Addendum to: Bonnard, B.; Caillau, J.-B.; Rifford, L. Convexity of injectivity domains on the ellipsoid of revolution: The oblate case. C. R. Acad. Sci. Paris, Ser. I 348 (2010), 1315–1318.
Geometric analysis of minimum time Keplerian orbit transfers
The minimum time control of the Kepler equation is considered. The typical application is the transfer of a satellite from an orbit around the Earth to another one, both orbits being elliptic. We recall the standard model to represent the system. Its Lie algebraic structure is first analyzed, and controllability is established for two different single-input subsystems, the control being oriented by the velocity or by the orthoradial direction. In both cases, a preliminary analysis of singular and regular extremals is also given, using the usual concept of order to classify the contacts. Moreover, the singularity of the multi-input model---which is a particular case of a subriemannian system…
Geometric and numerical techniques in optimal control of the two and three-body problems
The objective of this article is to present geometric and numerical techniques developed to study the orbit transfer between Keplerian elliptic orbits in the two-body problem or between quasi-Keplerian orbits in the Earth-Moon transfer when low propulsion is used. We concentrate our study on the energy minimization problem. From Pontryagin's maximum principle, the optimal solution can be found solving the shooting equation for smooth Hamiltonian dynamics. A first step in the analysis is to find in the Kepler case an analytical solution for the averaged Hamiltonian, which corresponds to a Riemannian metric. This will allow to compute the solution for the original Kepler problem, using a nume…
Differential pathfollowing for regular optimal control problems
International audience
A global optimality result with application to orbital transfer
The objective of this note is to present a global optimality result on Riemannian metrics $ds^2=dr^2+(r^2/c^2)(G(\vphi)d\theta^2+d\vphi^2)$. This result can be applied to the averaged energy minimization coplanar orbit transfer problem.
Smooth homotopies for single-input time optimal orbital transfer
International audience
Special issue in the honor of Bernard Bonnard. Part I and II
International audience
Injectivity domain of ellipsoid of revolution. The oblate case.
Study of the convexity of the injectivity domains on an oblate ellipsoid.
Smooth approximations of single-input controlled Keplerian trajectories: homotopies and averaging
International audience
Conjugate and cut loci in averaged orbital transfer
The objective of this Note is to describe the conjugate and cut loci associated with the averaged energy minimization problem in coplanar orbit transfer.
Second order optimality conditions in optimal control with applications
The aim of this article is to present the algorithm to compute the first conjugate point along a smooth extremal curve. Under generic assumptions, the trajectory ceases to be optimal at such a point. An implementation of this algorithm, called \texttt{cotcot}, is available online and based on recent developments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.