论文标题
平衡的大型系统迭代非线性控制的降级模型
Balanced Reduced-Order Models for Iterative Nonlinear Control of Large-Scale Systems
论文作者
论文摘要
我们提出了一个新框架，以设计高维非线性系统的控制器。该控件是通过迭代线性二次调节器（ILQR）设计的，该算法通过迭代在每个时间步骤上迭代将线性二次调节器应用于系统的局部线性化来计算控制。由于ILQR在计算上很昂贵，因此我们建议首先构建高维非线性系统的降级模型（ROM）。我们通过投影得出非线性ROM，其中基础是通过平衡截断（BT）和LQG平衡截断（LQG-BT）计算的。数值实验是在半消化的非线性汉堡方程式上进行的。我们发现，ILQR算法对由BT或LQG-BT构建的ROM产生良好的控制，而基于BT-ROM的控制器对于非常低维系统的LQG-BT略优于LQG-BT。
We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear quadratic regulator on the local linearization of the system at each time step. Since ILQR is computationally expensive, we propose to first construct reduced-order models (ROMs) of the high-dimensional nonlinear system. We derive nonlinear ROMs via projection, where the basis is computed via balanced truncation (BT) and LQG balanced truncation (LQG-BT). Numerical experiments are performed on a semi-discretized nonlinear Burgers equation. We find that the ILQR algorithm produces good control on ROMs constructed either by BT or LQG-BT, with BT-ROM based controllers outperforming LQG-BT slightly for very low-dimensional systems.
