ECE Seminar - Minimum Sample Data for Direct Data-driven Analysis and Adaptive LQR Design of Unknown Linear Systems

Abstract: Modern control theory has been firmly rooted in the state-space model, and then adopts system identification (SysId) followed by model-based control design methods. In this talk, we are motivated by two questions that possibly promote rethinking of this foundation: (a) whether SysId is indispensable to control design, and (b) if not, can we address it in a direct data-driven fashion (bypassing the SysId step)? In particular, via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum sample data for property ID (system analysis) of unknown linear systems. Specifically, the input sectional data is sufficiently rich for property ID if and only if it spans a linear subspace that contains a property dependent minimum linear subspace, any basis of which can also be easily used to form the minimum excitation input. Interestingly, we show that many structural properties can be identified with the minimum input that is however unable to complete SysId. Then, we propose an optimal data-enabled LQR formulation in the sense of achieving minimum regret of the quadratic cost, and design a novel data-enabled policy optimization (DeePO) method using only a batch of online persistently exciting (PE) data. Finally, we numerically validate the theoretical results and demonstrate the computational and sample efficiency of our method.