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 an exploration phase with the main feature that the exploration is optimized w.r.t. 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'.

中文翻译：

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顺序学习和控制：有针对性的探索以获得稳健的性能

我们提出了一种基于目标谐波探索和具有性能和激励保证的增益调度的新型不确定线性系统双重控制策略。在所提出的顺序方法中，在探索阶段之后实施鲁棒控制，其主要特征是探索针对鲁棒控制性能进行了优化。具体来说，我们利用最近关于使用谱线的有限激发的结果来确定勘探数据的最终有限激发的高概率下限。这为探索后剩余的模型不确定性提供了先验上限，可以在保证稳健性能的增益调度控制器设计中进一步加以利用。这导致了基于半定程序的设计，该设计计算具有有限激励界限和最小能量的探索策略，以及具有概率性能界限的增益调度控制器，可以在探索后实施。我们的方法的有效性及其优于普通随机探索策略的优势通过一个“难以学习”的系统示例得到证明。