Data-Driven Controller Design via Finite-Horizon Dissipativity

Given a single measured trajectory of a discrete-time linear time-invariant system, we present a framework for data-driven controller design for closed-loop finite-horizon dissipativity. First we parametrize all closed-loop trajectories using the given data of the plant and a model of the controller. We then provide an approach to validate the controller by verifying closed-loop dissipativity in the standard feedback loop based on this parametrization. The developed conditions allow us to state the corresponding controller synthesis problem as a quadratic matrix inequality feasibility problem. Hence, we obtain purely data-driven synthesis conditions leading to a desired closed-loop dissipativity property. Finally, the results are illustrated with a simulation example.