Gauss-Newton meets PANOC: A fast and globally convergent algorithm for nonlinear optimal control

TL;DR

This paper introduces a Gauss-Newton enhanced variant of PANOC for nonlinear optimal control, achieving faster convergence by efficiently solving Gauss-Newton steps via Riccati recursion, significantly improving speed over existing methods.

Contribution

It proposes a novel PANOC variant using Gauss-Newton directions for accelerated convergence and demonstrates efficient solution of these steps through LQR, enhancing real-time control performance.

Findings

More than twice as fast as L-BFGS PANOC on benchmark problems

Efficient Gauss-Newton step computation via Riccati recursion

Performance scales well with increasing horizon length

Abstract

PANOC is an algorithm for nonconvex optimization that has recently gained popularity in real-time control applications due to its fast, global convergence. The present work proposes a variant of PANOC that makes use of Gauss-Newton directions to accelerate the method. Furthermore, we show that when applied to optimal control problems, the computation of this Gauss-Newton step can be cast as a linear quadratic regulator (LQR) problem, allowing for an efficient solution through the Riccati recursion. Finally, we demonstrate that the proposed algorithm is more than twice as fast as the traditional L-BFGS variant of PANOC when applied to an optimal control benchmark problem, and that the performance scales favorably with increasing horizon length.