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

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.