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

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.

@article{roulet2025_2207.06362,
  title={ Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates },
  author={ Vincent Roulet and Siddhartha Srinivasa and Maryam Fazel and Zaid Harchaoui },
  journal={arXiv preprint arXiv:2207.06362},
  year={ 2025 }
}