标题： 基于在线自适应Koopman算子的非线性动力学模型预测控制 显示英文标题

标题： Model Predictive Control of Nonlinear Dynamics Using Online Adaptive Koopman Operators

摘要： 本文开发了一种基于Koopman算子的自适应数据驱动模型预测控制（MPC）方法。虽然MPC在各种工程领域中广泛应用，但如果控制模型与真实动力学之间的建模误差持续存在，控制器性能可能会下降，这在复杂非线性动力学中可能经常发生。自适应MPC技术在线学习模型，使控制器能够通过结合新可用数据来补偿建模误差。我们利用Koopman算子框架来制定一种自适应MPC技术，通过凸优化以计算效率高的方式校正模型差异。通过使用神经网络学习嵌入空间，Koopman算子模型能够实现准确的动力学建模。然而，这种复杂的模型形式通常会导致在线学习不稳定。为此，所提出的方法利用了目标网络的软更新技术，该技术用于强化学习（RL）中模型学习的稳定化。此外，我们还讨论了根据线性嵌入模型的具体描述应选择哪些参数作为在线更新参数。在典型非线性动力系统上的数值仿真表明，所提出的方法在与其他数据驱动MPC方法相比表现更优，同时通过利用Koopman算子实现了更高的计算效率。 显示英文摘要

摘要： This paper develops a methodology for adaptive data-driven Model Predictive Control (MPC) using Koopman operators. While MPC is ubiquitous in various fields of engineering, the controller performance can deteriorate if the modeling error between the control model and the true dynamics persists, which may often be the case with complex nonlinear dynamics. Adaptive MPC techniques learn models online such that the controller can compensate for the modeling error by incorporating newly available data. We utilize the Koopman operator framework to formulate an adaptive MPC technique that corrects for model discrepancies in a computationally efficient manner by virtue of convex optimization. With the use of neural networks to learn embedding spaces, Koopman operator models enable accurate dynamics modeling. Such complex model forms, however, often lead to unstable online learning. To this end, the proposed method utilizes the soft update of target networks, a technique used in stabilization of model learning in Reinforcement Learning (RL). Also, we provide a discussion on which parameters to be chosen as online updated parameters based on a specific description of linear embedding models. Numerical simulations on a canonical nonlinear dynamical system show that the proposed method performs favorably compared to other data-driven MPC methods while achieving superior computational efficiency through the utilization of Koopman operators.