Grammar-based representation and identification of dynamical systems

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model structure and complexity selection. In order to solve the combined model structure and model parameter estimation problem, a new representation of dynamical systems is proposed. The proposed representation is based on Tree Adjoining Grammar, a formalism that was developed from linguistic considerations. Using the proposed representation, the identification problem can be interpreted as a multiobjective optimization problem and we propose an Evolutionary Algorithm-based approach to solve it. A benchmark example is used to demonstrate the proposed approach. The achieved performance of the proposed method, without making use of knowledge of the system description, was comparable to that obtained by state-of-the-art non-linear system identification methods that do take advantage of correct selection of model structure and complexity based on a priori information.