论文标题
部分可观测时空混沌系统的无模型预测
Density Steering by Power Moments
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。
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a generalization of the conventional stochastic control problem where the uncertainty of the system state is usually characterized by a Gaussian distribution. We propose to use the power moments to turn the infinite-dimensional problem into a finite-dimensional one and to present an empirical control scheme. By the designed control law, the moment sequence of the controls at each time step is positive, which ensures the existence of the control for the moment system. We then realize the control at each time step as a function in analytic form by a convex optimization scheme, for which the existence and uniqueness of the solution have been proved in our previous paper. Two numerical examples are given to validate our proposed algorithm.
