2023/01/19 by Janani Venkatasubramanian, Johannes Köhler, Venkatasubramanian, Janani +5 · 2 citations
Engineering · Mathematics · #A priori and a posteriori #Advanced Control Systems Optimization #Artificial intelligence #Computer science #Control (management) #Control Systems and Identification #Control system #Control theory (sociology) #Engineering #FOS: Electrical engineering #Fault Detection and Control Systems #Gain scheduling #Leverage (statistics) #Machine learning #Mathematical optimization #Mathematics #Probabilistic logic #Robust control #Scheduling (production processes) #Systems and Control (eess.SY) #Upper and lower bounds #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2301.07995
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
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'.