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.

翻译：多胞体自编码器提供了状态在多胞体中的低维参数化表示。对于非线性偏微分方程，该方法可便捷地应用于低维线性参数变化（LPV）逼近，这类逼近通过状态相关Riccati方程解的级数展开，已被用于高效的非线性控制器设计。本文针对控制应用开发了一种多胞体自编码器，展示了其在LPV逼近非线性系统方面如何优于标准线性方法，并揭示了特定架构如何以极少的额外计算成本实现高阶级数展开。我们通过详尽的数值研究，阐明了该方法在大规模系统计算性非线性控制器设计中的特性与潜力。