Problem
Research questions and friction points this paper is trying to address.
Optimize nonlinear control using differentiable programming
Compare gradient descent, Gauss-Newton, Newton methods
Test algorithms on benchmarks like car racing
Iterative Linear Quadratic Optimization for Nonlinear Control: Differentiable Programming Algorithmic Templates
🤖 AI Summary
This work addresses discrete-time nonlinear optimal control problems by unifying classical algorithms—including gradient descent, Gauss–Newton, Newton’s method, and differential dynamic programming (DDP)—within a differentiable programming framework. Methodologically, it introduces the first modular, end-to-end differentiable algorithm template library built upon linear/quadratic approximations (e.g., LQR), enabled by automatic differentiation. Theoretically, it provides a unified derivation of computational complexity and sufficient optimality conditions across all methods. Practically, it incorporates adaptive line search and regularization strategies, and validates efficacy on benchmark tasks such as autonomous racing with a bicycle model. All implementations are open-sourced, demonstrating both efficient gradient propagation and strong generalization across diverse control problems.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Differentiable programming for nonlinear control
Iterative Linear Quadratic Optimization methods
Line-search and regularization strategies
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