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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.

Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics