Closed-loop Control from Data-Driven Open-Loop Optimal Control Trajectories

We show how the recent works on data driven open-loop minimum-energy control for linear systems can be exploited to obtain closed-loop piecewise-affine control laws, by employing a state-space partitioning technique which is at the basis of the static relatively optimal control. In addition, we propose a way for employing portions of the experimental input and state trajectories to recover information about the natural movement of the state and dealing with non-zero initial conditions. The same idea can be used for formulating several open-loop control problems entirely based on data, possibly including input and state constraints.