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.

中文翻译：

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大型系统迭代非线性控制的平衡降阶模型

我们提出了一个新的框架来设计用于高维非线性系统的控制器。通过迭代线性二次调节器（ILQR）设计控制，该算法通过在每个时间步长上将线性二次调节器迭代应用于系统的局部线性化来计算控制。由于ILQR的计算量很大，因此我们建议首先构建高维非线性系统的降阶模型（ROM）。我们通过投影导出非线性ROM，其中通过平衡截断（BT）和LQG平衡截断（LQG-BT）计算基础。在半离散非线性Burgers方程上进行了数值实验。我们发现ILQR算法可以很好地控制BT或LQG-BT构造的ROM，