A Sequential Quadratic Programming Perspective on Optimal Control

Abhijeet; Suman Chakravorty

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arXiv · 2605.25318

A Sequential Quadratic Programming Perspective on Optimal Control

Abhijeet·Suman Chakravorty

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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.

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BibTeX RIS

Abhijeet, Suman Chakravorty. 2026-05-25. A Sequential Quadratic Programming Perspective on Optimal Control. https://arxiv.org/abs/2605.25318

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