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arXiv · 2207.06362

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

Vincent Roulet·Siddhartha Srinivasa·Maryam Fazel·Zaid Harchaoui
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Abstract

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.

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Vincent Roulet, Siddhartha Srinivasa, Maryam Fazel, Zaid Harchaoui. 2022-07-13. Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates. https://arxiv.org/abs/2207.06362

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