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Local Convergence Behaviour of Generalized Gauss-Newton Multiple Shooting, Single Shooting and Differential Dynamic Programming
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Local Convergence Behaviour of Generalized Gauss-Newton Multiple Shooting, Single Shooting and Differential Dynamic Programming
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We revisit three classical numerical methods for solving unconstrained optimal control problems - multiple shooting, single shooting, and differential dynamic programming - and examine their local convergence behaviour. In particular, we show that all three methods converge with the same linear rate if a Gauss-Newton (GN), or more general a Generalized Gauss-Newton (GGN), Hessian approximation is used, which is the case in widely used implementations such as iLQR.
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