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

arXiv: https://arxiv.org/abs/2207.06362 · HTML: https://mlsanity.com/paper/2207.06362/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 13 Jul 2022.

## Builds on (most cited first, 4 of 4)

- [Optimization-Based Autonomous Racing of 1:43 Scale RC Cars](https://mlsanity.com/paper/1711.07300/) (2017)
- [Iterative Linearized Control: Stable Algorithms and Complexity Guarantees](https://mlsanity.com/paper/1908.07615/) (2019)
- [Accelerating Second-Order Differential Dynamic Programming for Rigid-Body Systems](https://mlsanity.com/paper/2103.03293/) (2021)
- [On Global and Local Convergence of Iterative Linear Quadratic Optimization Algorithms for Discrete Time Nonlinear Control](https://mlsanity.com/paper/2204.02322/) (2022)

## Built on by (most cited first, 1 of 1)

- [Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding](https://mlsanity.com/paper/2304.03907/) (2023)

## Abstract (arXiv)

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.