Session B1 - Computational Dynamics
July 15, 14:30 ~ 15:20 - Room 111
Validated numerics for robust space mission design
LAAS-CNRS, France - firstname.lastname@example.org
In this talk we overview several symbolic-numeric algorithms and software tools developed for robust space mission design. An application is the computation of validated impulsive optimal control for the rendezvous problem of spacecrafts, assuming a linear impulsive setting and a Keplerian relative motion. We combine theoretical tools in optimal control with computer algebra and validated numerics: this brings guarantees on numerical solutions, while preserving efficiency.
In particular, we focus on the a posteriori validation of trajectories solutions of the linear differential equations of the dynamics. These are computed as truncated Chebyshev series together with rigorously computed error bounds. A theoretical and practical complexity analysis of an a posteriori quasi-Newton validation method is presented. Several representative examples show the advantages of our algorithms as well as their theoretical and practical limits.
This talk is based on joint works with D. Arzelier, F. Bréhard, N. Brisebarre, N. Deak, J.-B. Lasserre, C. Louembet, A. Rondepierre, B. Salvy, R. Serra.