Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example, discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced-order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this article, a reduced-order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. The performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998 930.

中文翻译：

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线性降阶模型预测控制

模型预测控制器使用动力学模型来解决约束最优控制问题。然而，实时控制的计算要求限制了它们在具有低维模型的系统中的使用。然而，高维模型出现在许多环境中，例如，用于生成偏微分方程的有限维近似的离散化方法可以产生具有数千到数百万维的模型。在这种情况下，降阶模型 (ROM) 可以显着降低计算要求，但必须考虑模型逼近误差以保证控制器性能。在本文中，提出了一种降阶模型预测控制（ROMPC）方案来解决高维线性系统的鲁棒、输出反馈、约束最优控制问题。通过使用基于投影的 ROM 获得计算效率，并提供了对稳健约束满足和稳定性的保证。该方法的性能在几个示例的仿真中得到证明，包括利用尺寸为 998 930 的无粘性计算流体动力学模型的飞机控制问题。