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arXiv 2207.06362math.OCcs.LGcs.SYeess.SY
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非线性控制的迭代线性二次优化：可微编程算法模板

Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates

Google Brain, Seattle, USA（谷歌大脑）；Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, USA（保罗·G·艾伦计算机科学与工程学院）；Department of Electrical and Computer Engineering, University of Washington, Seattle, USA（电气与计算机工程系）；Department of Statistics University of Washington, Seattle, USA（统计学系）

Vincent Roulet, Siddhartha Srinivasa, Maryam Fazel, Zaid Harchaoui

备注：
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. Published in the Open Journal of Mathematical Optimization in 2024
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AI总结：

本文将梯度下降、Gauss-Newton、Newton和微分动态规划等非线性控制算法统一到可微编程框架中，分析其共享组件、计算复杂度及正则化变体，并通过自动驾驶赛车等基准验证性能。

摘要：

迭代优化算法依赖于获取目标函数信息。在可微编程框架中，梯度等信息可以从计算图自动推导。我们探索了通常采用线性和/或二次近似的非线性控制算法如何有效地融入该框架。我们的方法阐明了在离散时间非线性控制背景下，梯度下降、Gauss-Newton、Newton和微分动态规划方法之间的共享组件与差异。此外，我们提出了这些算法的线搜索策略和正则化变体，并对其计算复杂度进行了全面分析。我们在各种非线性控制基准上研究了上述算法的性能，包括使用简化汽车模型的自动驾驶赛车仿真。所有实现均以可微编程语言编写的软件包形式公开提供。

英文摘要：

Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We explore how nonlinear control algorithms, often employing linear and/or quadratic approximations, can be effectively cast within this framework. Our approach illuminates shared components and differences between gradient descent, Gauss-Newton, Newton, and differential dynamic programming methods in the context of discrete time nonlinear control. Furthermore, we present line-search strategies and regularized variants of these algorithms, along with a comprehensive analysis of their computational complexities. We study the performance of the aforementioned algorithms on various nonlinear control benchmarks, including autonomous car racing simulations using a simplified car model. All implementations are publicly available in a package coded in a differentiable programming language.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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