Mathematics > Optimization and Control
arXiv:2207.06362 (math)
[Submitted on 13 Jul 2022]
Title:Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates
View a PDF of the paper titled Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates, by Vincent Roulet and 3 other authors
View PDFAbstract:We present the implementation of nonlinear control algorithms based on linear and quadratic approximations of the objective from a functional viewpoint. We present a gradient descent, a Gauss-Newton method, a Newton method, differential dynamic programming approaches with linear quadratic or quadratic approximations, various line-search strategies, and regularized variants of these algorithms. We derive the computational complexities of all algorithms in a differentiable programming framework and present sufficient optimality conditions. We compare the algorithms on several benchmarks, such as autonomous car racing using a bicycle model of a car. The algorithms are coded in a differentiable programming language in a publicly available package.
| Comments: | This is a companion report to the arXiv report "Complexity Bounds of Iterative Linear Quadratic Optimization Algorithms for Discrete Time Nonlinear Control" <arXiv:2204.02322> by the same authors |
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY) |
| MSC classes: | 68Q25, 49M37 |
| ACM classes: | G.1.6 |
| Cite as: | arXiv:2207.06362 [math.OC] |
| (orarXiv:2207.06362v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2207.06362 arXiv-issued DOI via DataCite |
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View a PDF of the paper titled Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates, by Vincent Roulet and 3 other authors
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