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arXiv 2012.03384eess.SYcs.SY
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线性降阶模型预测控制

Linear Reduced Order Model Predictive Control

Joseph Lorenzetti, Andrew McClellan, Charbel Farhat, Marco Pavone

AI总结:

针对高维线性系统最优控制的计算瓶颈,提出基于投影降阶模型的鲁棒输出反馈预测控制方案,给出稳定性与约束满足保证,并在含近百万维流体模型的飞行器控制仿真中验证有效性。

摘要:

模型预测控制器利用动力学模型求解带约束的最优控制问题,但实时控制的计算需求使其应用局限于低维模型系统。然而,高维模型在诸多场景中十分常见,例如为偏微分方程生成有限维近似的离散化方法,会产生维度从数千到数百万的模型。在此类情况下,降阶模型(ROMs)可大幅降低计算需求,但必须考虑模型近似误差以保证控制器性能。本研究提出一种降阶模型预测控制(ROMPC)方案,用于求解高维线性系统的鲁棒输出反馈带约束最优控制问题。该方案通过基于投影的ROMs实现计算效率提升,并给出了鲁棒约束满足性和稳定性的保证。研究通过多个仿真示例验证了该方法的性能,其中包括一个利用维度为998930的无粘计算流体动力学模型的飞行器控制问题。

英文摘要:

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 work, 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. 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.

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