The canonical controller approach to data-driven update of state feedback gain

In this paper, a data-driven update or design method of desirable state feedback gains is presented. By utilizing the “canonical controller” developed in the behavioral framework, we derive a fundamental kernel representation of the canonical controller which yields a desirable state feedback gain and is also compatible with the trajectory of the system. We also show that such a kernel representation for the canonical controller can be obtained by minimizing a cost function which is linearly represented with respect to only one-shot experimental data. Finally, an illustrative example is given to show the validity of our proposed method.