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’.

中文翻译：

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顺序学习与控制：稳健性能的针对性探索


我们针对不确定线性系统提出了一种新颖的双控制策略，该策略基于有针对性的谐波探索和具有性能和激励保证的增益调度。在所提出的顺序方法中，鲁棒控制是在探索之后实施的，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，我们利用谱线利用有限激励的最新结果来确定勘探数据的有限激励的高概率下界。这提供了探索后剩余模型不确定性的先验上限，可以在保证稳健性能的增益调度控制器设计中进一步利用该上限。这导致了基于半定程序的设计，该设计计算具有有限激励边界和最小能量的探索策略，以及具有可在探索后实现的概率性能边界的增益调度控制器。我们的方法的有效性及其相对于常见随机探索策略的优势通过一个“难以学习”的系统的例子得到了证明。