Recurrent Model Predictive Control: Learning an Explicit Recurrent Controller for Nonlinear Systems
Zhengyu Liu, Jingliang Duan, Wenxuan Wang, Shengbo Eben Li, Yuming Yin, Ziyu Lin, Bo Cheng
Abstract
This article proposes an offline control algorithm, called recurrent model predictive control, to solve large-scale nonlinear finite-horizon optimal control problems. It can be regarded as an explicit solver of traditional model predictive control (MPC) algorithms, which can adaptively select appropriate model prediction horizon according to current computing resources, so as to improve the policy performance. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The output of the learned policy network after <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> recurrent cycles corresponds to the nearly optimal solution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -step MPC. A policy optimization objective is designed by decomposing the MPC cost function according to the Bellman’s principle of optimality. The optimal recurrent policy can be obtained by directly minimizing the designed objective function, which is applicable for general nonlinear and noninput-affine systems. Both simulation-based and real-robot path-tracking tasks are utilized to demonstrate the effectiveness of the proposed method.