Abstract
This paper presents variations of the Successive Backward Sweep (SBS) method for solving nonlinear optimal control problems with terminal constraints. The state-costate differential equations are linearized and discretized explicitly in time by a truncated Magnus series representation of the state transition. These discrete exponential maps are propagated, backwards in time, by the sweep method. Two variants of the method are implemented to test for the Jacobi sufficient condition and achieve convergence to local optimal solutions. Where required, the problems are regularized to ensure satisfaction of the convexity conditions by modifying the associated Hessian. The performance of the Magnus series-based SBS method is compared with that of a non-symplectic 5 th order Runge-Kutta method on three examples: a highly nonlinear, two-dimensional problem, a hypersensitive problem, and an atmospheric reentry guidance problem.
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