The optimal feedback control problem for low-thrust trajectories with modulated inverse-square-distance radial thrust is studied in this paper. The problem is tackled by applying a generating-function method devised for linear systems. Instead of deriving open-loop solutions, arising from the two-point boundary-value problems in which the classical optimal control is stated, this technique allows us to obtain analytical closed-loop control laws. The idea behind this work consists of applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear dynamic system into a linear system of ordinary differential equations written in new variables. The generating-function technique is then applied to this new dynamic system, the optimal feedback control problem is solved, and the variables are transformed back into the original. Thus, we avoid the problem of expanding the vector field and truncating higher-order terms, because no remainders are lost in the approach undertaken. Practical examples are used to show the usefulness of the derived solution for modulated, inverse-square-distance, radially accelerated orbits.

Analytical Solution of Optimal Feedback Control for Radially Accelerated Orbits

TOPPUTO, FRANCESCO;BERNELLI ZAZZERA, FRANCO
2008-01-01

Abstract

The optimal feedback control problem for low-thrust trajectories with modulated inverse-square-distance radial thrust is studied in this paper. The problem is tackled by applying a generating-function method devised for linear systems. Instead of deriving open-loop solutions, arising from the two-point boundary-value problems in which the classical optimal control is stated, this technique allows us to obtain analytical closed-loop control laws. The idea behind this work consists of applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear dynamic system into a linear system of ordinary differential equations written in new variables. The generating-function technique is then applied to this new dynamic system, the optimal feedback control problem is solved, and the variables are transformed back into the original. Thus, we avoid the problem of expanding the vector field and truncating higher-order terms, because no remainders are lost in the approach undertaken. Practical examples are used to show the usefulness of the derived solution for modulated, inverse-square-distance, radially accelerated orbits.
File in questo prodotto:
File Dimensione Formato  
TOPPF03-08.pdf

Accesso riservato

: Altro materiale allegato
Dimensione 377.34 kB
Formato Adobe PDF
377.34 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/11311/526740
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 8
social impact