Data-driven control of continuous-time systems: A synthesis-operator approach
It addresses the challenge of data-driven control for continuous-time systems without requiring state derivatives, offering a novel theoretical framework for practitioners.
This paper develops a data-driven control framework for continuous-time systems using synthesis operators, avoiding state derivative estimation and direct sampling. It provides necessary and sufficient conditions for data informativity in system identification and stabilization, both in noise-free and noisy cases, with finite-dimensional matrix characterizations.
This paper addresses data-driven control of continuous-time systems. We develop a framework based on synthesis operators associated with state and input trajectories. A key advantage of the proposed method is that it does not require the state derivative and uses continuous-time data directly without sampling or filtering. First, systems consistent with the data are represented in terms of synthesis operators, into which the data trajectories are embedded. Next, we characterize data informativity properties for system identification and for stabilization in the noise-free case. Finally, we establish a necessary and sufficient condition for noisy data to be informative for quadratic stabilization. All these informativity characterizations are formulated in terms of finite-dimensional matrices, by leveraging the finite-rank structure of the synthesis operators.