Data-Driven Control Design With LMIs and Dynamic Programming

The goal of this paper is to study model-free data-driven control evaluation and design strategies for discrete-time linear time-invariant systems, where the system model is unknown. In particular, our main contribution is twofold: 1) new state-input exploration and data collection schemes from experiences; 2) new data-driven linear matrix inequalities and dynamic programming methods for stabilization and optimal control problems. The proposed exploration and data collection schemes theoretically guarantee to acquire sufficient information from the system’s state-input trajectories that can solve the underlying control design problems. We prove that under mild assumptions, as more and more data is accumulated, the collected data can solve the problems with higher probability along with the proposed algorithms.