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 NN recurrent cycles corresponds to the nearly optimal solution of NN-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.

中文翻译：

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循环模型预测控制：学习非线性系统的显式循环控制器


本文提出了一种称为循环模型预测控制的离线控制算法，用于解决大规模非线性有限范围最优控制问题。它可以看作是传统模型预测控制（MPC）算法的显式求解器，可以根据当前的计算资源自适应地选择合适的模型预测范围，从而提高策略性能。我们的算法采用循环函数来近似最优策略，它将系统状态和参考值直接映射到控制输入。经过 NN 个循环周期后学习到的策略网络的输出对应于 NN 步 MPC 的近乎最优解。根据贝尔曼最优原理分解MPC成本函数来设计策略优化目标。通过直接最小化设计的目标函数可以得到最优的循环策略，适用于一般的非线性和非输入仿射系统。基于仿真和真实机器人路径跟踪任务都被用来证明所提出方法的有效性。