论文标题
控制库普曼嵌入模型的控制知觉
Control-aware Learning of Koopman Embedding Models
论文作者
论文摘要
为基于Koopman操作员的模型提出了一种学习方法，其目的是改善闭环控制行为。一种基于神经网络的方法用于发现一个可观察到的空间，其中非线性动力学是线性嵌入的。尽管使用这种复杂的状态到观察的图可以预期准确的状态预测，但是当模型被部署在闭环环境中时，可能会引入不良的副作用。这是由于线性嵌入过程中的建模或残留误差，与状态预测相比，这可能以不同的方式表现出来。为此，提出了一种技术来完善最初受过训练的模型，目的是改善模型的闭环行为，同时保留在初始学习中获得的状态预测准确性。最后，提出了一种简单的数据采样策略来使用从连续函数进行确定采样的输入，从而导致非线性动力学系统的控制器性能的进一步改进。提供了几个数值示例，以显示该方法的功效。
A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly embedded. While accurate state predictions can be expected with the use of such complex state-to-observable maps, undesirable side-effects may be introduced when the model is deployed in a closed-loop environment. This is because of modeling or residual error in the linear embedding process, which can manifest itself in a different manner compared to the state prediction. To this end, a technique is proposed to refine the originally trained model with the goal of improving the closed-loop behavior of the model while retaining the state-prediction accuracy obtained in the initial learning. Finally, a simple data sampling strategy is proposed to use inputs deterministically sampled from continuous functions, leading to additional improvements in the controller performance for nonlinear dynamical systems. Several numerical examples are provided to show the efficacy of the proposed method.
