Information-triggered learning with application to learning-based predictive control

Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the abundance of data becomes overwhelming. To address this issue, this work proposes an information-triggered learning framework and a corresponding learning-based 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 evaluating the incremental information in a data sample, where the incremental information is quantified by its effects on shrinking the parametric uncertainty set. Next, after introducing a stability criterion using the set-membership estimate of the system dynamics, a robust learning-based predictive controller (LPC) is designed by minimizing a worst-case cost function. The closed-loop stability of the LPC equipped with the information-triggered learning protocol is discussed within a high-probability framework. Finally, comparative numerical experiments are performed to verify the validity of the proposed approach.