Optimal experiment design in closed loop with unknown, nonlinear and implicit controllers using stealth identification

We present a novel optimal experiment design method that is applicable to linear time-invariant systems regulated by unknown, nonlinear and implicitly-defined controllers. Current methods require an explicit expression for the controller in order to construct the optimal excitation spectrum. Consequently, these are limited to linearly-controlled systems. The identification scheme suggested in this paper circumvents the aforementioned requirement by ensuring that the excitation signal remains unnoticed by the controller, i.e., the identification data is gathered in an open-loop fashion. Our theoretical analysis is complemented with a numerical study on a six-parameter, single-input single-output linear system controlled by an MPC. We find that our method generates least-costly excitation signals which deliver identified models that lie close to the true system whilst honoring quality constraints, validating the novel optimal experiment design framework.