  Data-driven control has attracted lots of attention in recent years,
especially for plants that are difficult to model based on first principles. In
particular, a key issue in data-driven approaches is how to make efficient use
of data as the abundance of data becomes overwhelming. To address this issue,
this work proposes an innovation-triggered learning framework and a
corresponding data-driven controller design approach with guaranteed stability.
Specifically, we consider a linear time-invariant system with unknown dynamics.
A set-membership approach is introduced to learn a parametric uncertainty set
for the unknown dynamics. Then, a data selection mechanism is proposed by
online evaluating the innovation contained in the sampled data, wherein the
innovation is quantified by its effect of shrinking the parametric uncertainty
set. Next, after introducing a stability criterion using the set-membership
estimate of the system dynamics, a robust data-driven predictive controller is
designed by minimizing a worst-case cost function. The closed-loop stability of
the data-driven predictive controller equipped with the innovation-triggered
learning protocol is discussed within a high probability framework. Finally,
comparative numerical experiments are performed to verify the validity of the
proposed approach, and the characteristics and the design principle of the
learning hyper-parameter are also discussed.
