  The goal of this paper is to develop data-driven control design and
evaluation strategies based on linear matrix inequalities (LMIs) and dynamic
programming. We consider deterministic discrete-time LTI systems, where the
system model is unknown. We propose efficient data collection schemes from the
state-input trajectories together with data-driven LMIs to design
state-feedback controllers for stabilization and linear quadratic regulation
(LQR) problem. In addition, we investigate theoretically guaranteed exploration
schemes to acquire valid data from the trajectories under different scenarios.
In particular, we prove that as more and more data is accumulated, the
collected data becomes valid for the proposed algorithms with higher
probability. Finally, data-driven dynamic programming algorithms with
convergence guarantees are then discussed.
