Table of Contents
ISRN Aerospace Engineering
Volume 2013 (2013), Article ID 950912, 7 pages
Research Article

Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy

Received 25 June 2013; Accepted 27 August 2013

Academic Editors: H. Baoyin, C. Bigelow, and D. Yu

Copyright © 2013 Francesco Topputo and Franco Bernelli-Zazzera. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as “approximating sequence of Riccati equations.” Sample problems in astrodynamics are treated to show the effectiveness of the method, whose limitations are also discussed.