Grammar-based Representation and Identification of Dynamical Systems

Abstract

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 a Evolutionary Algorithm-based approach to solve the problem. A benchmark example is used to demonstrate the proposed approach. The results were found to be comparable to that obtained by stateof-the-art non-linear system identification methods, without making use of knowledge of the system description.

Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming

“…For completeness, we provide a brief description of the proposed modelling approach. A more detailed account can be found in [22].…”

“…Algorithm 1 Multi-objective data-driven modelling using TAG and GP [22] Require: population size M > 0, number of iterations L > 0, grammar G, probabilities of crossover and mutation p c , p m 1: Initialize population X (0) , l = 0, X Compute multi-objective fitness of models in X (l)…”

“…An approach for data-driven modelling of non-linear systems using Genetic Programming (GP) was presented in [22]. The proposed method makes use of fundamental building blocks to generate model structures, but unlike other equation discovery methods, the construction of new model structures is guided by Tree Adjoining Grammar (TAG) (see [23]).…”

“…More crucially, the lack of a suitable noise model may also result in a bias in the estimated model (e.g., see [6]). The work in [22] was inspired by [3], where the authors used TAG-guided GP to solve a static symbolic regression problem.…”

“…In this paper, we apply the method presented in [22] to three case studies involving real physical systems. The case studies involve modelling of the:…”