Direct closed-loop identification of continuous-time systems using fixed-pole observer model

This paper provides a method for obtaining a continuous-time model of a target system in closed-loop from input-output data alone, in the case where no knowledge of the controllers nor excitation signals is available and I/O data may suffer from unknown offsets. The proposed method is based on a fixed-pole observer model, which is a reasonable continuous-time version corresponding to the innovation model in discrete-time and allows the identification of unstable target systems. Furthermore, it is shown that the proposed method can be attributed to a convex optimization problem by fixing the observer poles. The method is within the framework of the stabilized output error method and shares usability advantages such as robustness to noise with complex dynamics and applicability to a wide class of models. The effectiveness of the method is illustrated through numerical examples.