A Sequential Quadratic Programming Perspective on Optimal Control
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917530359037952 |
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| author | Abhijeet Chakravorty, Suman |
| author_facet | Abhijeet Chakravorty, Suman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Sequential Quadratic Programming Perspective on Optimal Control Abhijeet Chakravorty, Suman Optimization and Control 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. |
| title | A Sequential Quadratic Programming Perspective on Optimal Control |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.25318 |