论文标题
部分可观测时空混沌系统的无模型预测
Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We propose a data-driven method for controlling the frequency and convergence rate of black-box nonlinear dynamical systems based on the Koopman operator theory. With the proposed method, a policy network is trained such that the eigenvalues of a Koopman operator of controlled dynamics are close to the target eigenvalues. The policy network consists of a neural network to find a Koopman invariant subspace, and a pole placement module to adjust the eigenvalues of the Koopman operator. Since the policy network is differentiable, we can train it in an end-to-end fashion using reinforcement learning. We demonstrate that the proposed method achieves better performance than model-free reinforcement learning and model-based control with system identification.
