Data-driven Dynamic Relatively Optimal Control

We show how the recent works on data-driven open-loop minimum-energy control for linear systems can be exploited to obtain closed-loop control laws in the form of linear dynamic controllers that are relatively optimal. Besides being stabilizing, they achieve the optimal minimum-energy trajectory when the initial condition is the same as the open-loop optimal control problem. The order of the controller is N−n, where Nis the length of the optimal open-loop trajectory, and nis the order of the system. The same idea can be used for obtaining a relatively optimal controller, entirely based on data, from open-loop trajectories starting from up to nlinearly independent initial conditions.