Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.

翻译：许多工程问题都会产生高度非线性非线性系统,原因是管理部分差异方程式的半分化,例如通过有限元素法。这些系统的复杂性对直接应用自动控制提出了计算上的挑战。虽然模型的减少在控制中看到了无处不在的应用,但在这种环境下使用非线性模型的减少方法仍然很困难。问题在于如何在高忠诚控制减序模型中保留非线性动态的结构。在这项工作中,我们利用了光谱子折叠理论的最新进展,以便在明确界定的假设下使模型的减少能够有效地综合反馈控制器。