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We revisit three classical numerical methods for solving unconstrainedoptimal control problems - multiple shooting, single shooting, and differentialdynamic programming - and examine their local convergence behaviour. Inparticular, we show that all three methods converge with the same linear rateif a Gauss-Newton (GN), or more general a Generalized Gauss-Newton (GGN),Hessian approximation is used, which is the case in widely used implementationssuch as iLQR.

Local Convergence Behaviour of Generalized Gauss-Newton Multiple Shooting, Single Shooting and Differential Dynamic Programming