Autonomous energy-based model order selection in parameter state space identification via cross Gramian and symmetrizer

Subspace system identification is a well known process for modeling complex dynamical systems based on measured data. A key challenge in this domain is determining the dimensionality of the state space, if it is immeasurable, which is critical for estimating a reliable model. Classically, a stabilization diagram is created to select the appropriate model order, which involves subjective human judgment. This can lead to inconsistencies and errors. This paper presents a novel approach to select the model order, called Autonomous Model Order Selection (AMOS), that takes into account the estimated energy of the states. This method utilizes the cross Gramian, which captures the interaction between the system’s states and it is input/output dynamics, and a symmetrizer. The energy error is proposed as a measure to quantify the quality of the approximation of the identified system with respect to the observed measurement. A less subjective and more systematic measure is provided, validated by a simulation and real laboratory measurements of a bending beam. The proposed method is limited to square systems (the number of inputs is equal to the number of outputs).