论文标题
非线性控制的迭代线性二次优化：可区分的编程算法模板
Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates
论文作者
论文摘要
迭代优化算法取决于访问有关目标函数的信息。在可区分的编程框架中，这些信息（例如梯度）可以自动从计算图中得出。我们探讨如何在此框架内有效地施放非线性控制算法，通常采用线性和/或二次近似值。我们的方法阐明了在离散时间非线性控制的背景下，梯度下降，高斯 - 纽顿，牛顿和差异动态编程方法之间的共享组件和差异。此外，我们介绍了这些算法的线路搜索策略和正则变体，以及对其计算复杂性的全面分析。我们研究了上述各种非线性控制基准的上述算法的性能，包括使用简化的汽车模型的自主赛车模拟。所有实现均以用可区分编码语言编码的软件包公开使用。
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.
