Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope. For nonlinear PDEs, this is readily applied to low-dimensional linear parameter-varying (LPV) approximations as they have been exploited for efficient nonlinear controller design via series expansions of the solution to the state-dependent Riccati equation. In this work, we develop a polytopic autoencoder for control applications and show how it outperforms standard linear approaches in view of LPV approximations of nonlinear systems and how the particular architecture enables higher order series expansions at little extra computational effort. We illustrate the properties and potentials of this approach to computational nonlinear controller design for large-scale systems with a thorough numerical study.

中文翻译：

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用于低维线性参数变化近似和非线性反馈设计的深度多面体自动编码器

多面体自动编码器提供多面体状态的低维参数化。对于非线性偏微分方程，这很容易应用于低维线性变参数 (LPV) 近似，因为它们已通过状态相关 Riccati 方程的解的级数展开来用于高效的非线性控制器设计。在这项工作中，我们开发了一种用于控制应用的多面自动编码器，并展示了它如何在非线性系统的 LPV 近似方面优于标准线性方法，以及特定的架构如何以很少的额外计算工作量实现更高阶级数展开。我们通过全面的数值研究说明了这种大规模系统计算非线性控制器设计方法的特性和潜力。