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arXiv · 2606.01487

Global Convergence of a Line-Search Filter Differential Dynamic Programming Method

Ming Xu·Iman Shames
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Abstract

In this article, we establish the global convergence properties of the FilterDDP algorithm, which extends the discrete-time differential dynamic programming (DDP) algorithm of Mayne and Jacobson [\emph{International Journal of Control}, 3, (1966), pp. 85-95] to handle nonlinear constraints over states and controls, in addition to the dynamics. FilterDDP adopts a line-search filter procedure for step acceptance. However, instead of a damped Newton step applied in the general nonlinear programming setting, the computation of a trial point involves applying a backward recursion and a forward simulation. We establish the global convergence of FilterDDP by showing that for a subset of constrained optimal control problems, the this backward-forward procedure satisfies the same properties as a Newton step for the purpose of establishing global convergence of a line-search filter method, following the analysis of W\"achter and Biegler [\emph{SIAM Journal on Optimization}, 16 (2005), pp. 1-31].

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Ming Xu, Iman Shames. 2026-05-31. Global Convergence of a Line-Search Filter Differential Dynamic Programming Method. https://arxiv.org/abs/2606.01487

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