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

• URL: http://arxiv.org/abs/2606.01487v1
• Date: Sun, 31 May 2026 23:03:24 GMT
• Title: Global Convergence of a Line-Search Filter Differential Dynamic Programming Method
• Abstract summary: FilterDDP is extended to handle nonlinear constraints over states and controls.<n>A backward-forward procedure satisfies the same properties as a Newton step for a subset of constrained optimal control problems.
• Score: 2.4977965164085068
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Wächter and Biegler [\emph{SIAM Journal on Optimization}, 16 (2005), pp. 1-31].

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