A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.

High Order Optimal Control of Space Trajectories with Uncertain Boundary Conditions

DI LIZIA, PIERLUIGI;ARMELLIN, ROBERTO;BERNELLI ZAZZERA, FRANCO;
2014-01-01

Abstract

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.
2014
Optimal control, Space trajectories, High-order methods, Differential algebra, Uncertain boundary conditions
File in questo prodotto:
File Dimensione Formato  
DILIP01-14.pdf

Accesso riservato

: Publisher’s version
Dimensione 1.36 MB
Formato Adobe PDF
1.36 MB Adobe PDF   Visualizza/Apri
DILIP_OA_01-14.pdf

Open Access dal 02/02/2016

Descrizione: Paper open access
: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 518.13 kB
Formato Adobe PDF
518.13 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/735769
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 32
  • ???jsp.display-item.citation.isi??? 22
social impact