Frequency-domain data-driven control design in the Loewner framework

Data-driven control design in the Loewner framework: Dealing with stability and noise

“…That is how model reduction is done through the Loewner framework. In [11], the controller model is directly reduced to the objective order n but then the obtained controller is not necessarily stable and its poles can be affected by the noise.…”

“…As detailed in [11], the L-DDC algorithm allows to identify a controller, without any a priori structure. The specifications are expressed as a reference transfer function M which represents the desired behavior in closed-loop.…”

“…This was not possible in the original version of the L-DDC algorithm proposed in [11] but, in this paper, we propose to use the algorithm introduced in [14] to ensure the stability of the identified controller. Note that this algorithm has already been combined with the Loewner framework in [16] in the area of model reduction.…”

“…Another method is the L-DDC algorithm, originally proposed in [11]. This is a one shot method based on frequencydomain data that does not require a initial stabilizing controller.…”

“…Then, the proposed method to design a controller on the basis of frequencydomain data is exposed in Section IV. In comparison with [11], the main contribution is to allow to treat noisy data and to enforce the stability of the controller, these two aspects are detailed in Section IV. Finally, an academic example is considered in Section V to illustrate the method.…”