Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

Abstract

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.