Abstract:This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these approaches, centered on the understanding that each method ultimately solves a sequence of quadratic programs. Building upon previous comparative works, this paper contributes additional mathematical explanations and results to the analysis.
In particular, it is shown that iLQR is a principled Sequential Quadratic Programming (SQP) approach, rather than merely an approximation of DDP that neglects Hessian terms. This characteristic guarantees that iLQR will always produce a cost-descent direction and converge to an optimum, under some mild assumptions. In contrast, Newton's method and DDP lack these guarantees, especially when initialized far from an optimum. A series of numerical examples are presented to corroborate the mathematical reasoning and analysis developed in the paper.
| Subjects: | Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.25318 [math.OC] |
| (or arXiv:2605.25318v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25318 arXiv-issued DOI via DataCite (pending registration) |
From: Fnu Abhijeet [view email]
[v1]
Mon, 25 May 2026 00:42:41 UTC (750 KB)
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