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arXiv 2405.02809eess.SYcs.SY
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最优控制总能从更好的预测中受益吗?一种预测性最优控制的分析框架

Does Optimal Control Always Benefit from Better Prediction? An Analysis Framework for Predictive Optimal Control

Xiangrui Zeng, Cheng Yin, Zhouping Yin

AI总结:

本文提出预测性最优控制分析框架,引入隐藏预测状态概念,证明均方误差和似然无法保证预测误差与控制代价的单调关系,建议用控制性能评估预测器。

摘要:

“预测 + 最优控制”方案在汽车、交通、机器人和建筑控制等许多应用中表现出良好的性能。在实际中,预测结果在最优控制设计过程中被简单地认为是正确的。然而,在现实中,这些预测可能永远不会完美。在传统的随机最优控制表述下,很难回答诸如“如果预测是错误的会怎样”这类问题。本文提出了一种预测性最优控制的分析框架,其中关于未来的主观信念不再被认为是完美的。提出了一种称为隐藏预测状态的新概念,以建立预测器、主观信念、控制策略和客观控制性能之间的联系。基于该框架,分析了预测器评估问题。考虑了三种常用的预测器评估指标,包括均方误差、遗憾值和对数似然。结果表明,使用均方误差或使用似然都不能保证预测器误差与最优控制代价之间存在单调关系。为了保证控制代价的改善,建议应结合控制性能来评估预测器,例如使用最优控制代价或遗憾值来评估预测器。文中提供了数值示例以及使用真实世界驾驶数据的汽车应用示例来说明这些思想和结果。

英文摘要:

The ``prediction + optimal control'' scheme has shown good performance in many applications of automotive, traffic, robot, and building control. In practice, the prediction results are simply considered correct in the optimal control design process. However, in reality, these predictions may never be perfect. Under a conventional stochastic optimal control formulation, it is difficult to answer questions like ``what if the predictions are wrong''. This paper presents an analysis framework for predictive optimal control where the subjective belief about the future is no longer considered perfect. A novel concept called the hidden prediction state is proposed to establish connections among the predictors, the subjective beliefs, the control policies and the objective control performance. Based on this framework, the predictor evaluation problem is analyzed. Three commonly-used predictor evaluation measures, including the mean squared error, the regret and the log-likelihood, are considered. It is shown that neither using the mean square error nor using the likelihood can guarantee a monotonic relationship between the predictor error and the optimal control cost. To guarantee control cost improvement, it is suggested the predictor should be evaluated with the control performance, e.g., using the optimal control cost or the regret to evaluate predictors. Numerical examples and examples from automotive applications with real-world driving data are provided to illustrate the ideas and the results.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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