序列学习与控制：面向鲁棒性能的定向探索
Sequential learning and control: Targeted exploration for robust performance
AI总结：
针对不确定线性系统，提出一种基于定向谐波探索和增益调度的双重控制策略，通过优化探索以最小能量实现有限激励并保证鲁棒性能，优于随机探索。
摘要：
我们提出了一种针对不确定线性系统的新型双重控制策略，该策略基于定向谐波探索和增益调度，并具有性能与激励保证。在所提出的序列方法中，鲁棒控制在探索之后实施，其主要特征是探索过程针对鲁棒控制性能进行了优化。具体而言，我们利用关于使用谱线有限激励的最新结果，来确定探索数据最终有限激励的高概率下界。这为探索后剩余的模型不确定性提供了先验上界，可进一步用于保证鲁棒性能的增益调度控制器设计。由此产生了一种基于半定规划的设计，它计算出具有有限激励边界和最小能量的探索策略，以及一个可在探索后实施、具有概率性能边界的增益调度控制器。我们通过一个“难以学习”的系统示例，证明了该方法的有效性及其相较于常见随机探索策略的优势。
英文摘要：
We present a novel dual control strategy for uncertain linear systems based on targeted harmonic exploration and gain-scheduling with performance and excitation guarantees. In the proposed sequential approach, robust control is implemented after exploration with the main feature that the exploration is optimized with respect to the robust control performance. Specifically, we leverage recent results on finite excitation using spectral lines to determine a high probability lower bound on the resultant finite excitation of the exploration data. This provides an a priori upper bound on the remaining model uncertainty after exploration, which can further be leveraged in a gain-scheduling controller design that guarantees robust performance. This leads to a semidefinite program-based design which computes an exploration strategy with finite excitation bounds and minimal energy, and a gain-scheduled controller with probabilistic performance bounds that can be implemented after exploration. The effectiveness of our approach and its benefits over common random exploration strategies are demonstrated with an example of a system which is 'hard to learn'.
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