Data-driven control for linear systems using reachable sets

We consider the problem of designing controllers for linear time-invariant systems based on measured data (without explicitly identifying the matrices of the system). We discuss two methods for stabilization: forward and backward reachable set computations. In the former one, we collect trajectories of the system for different given initial states and compute control inputs enforcing some stability conditions. Then, using the offline computations, we design for any initial condition the online control inputs that stabilize the system. In the second approach, we synthesize offline a contracting set and use it to define online the system's control inputs. We have illustrated the efficiency of our results through an example.