Cluster Based Multiobjective Genetic Programming in Nonlinear Systems Identification

Multivariable nonlinear systems identification is addressed, in the following, by means of enhanced multiobjective evolutionary optimisation. The paper suggests a customised genetic programming algorithm that generates nonlinear linear in parameter models, according to a mathematical pattern that has been proven to be a universal approximator. In order to efficiently exploit the parameter wise linearity, the authors propose a symbiosis between the genetic operators and a local optimisation procedure based on QR decomposition. This hybridisation provides simultaneous structure selection and parameter computation, whilst facilitating the unsupervised exploration of the search space. Model assessment is conducted relative to accuracy and parsimony evaluation criteria. The latter has been specifically tailored to encourage the gradual elimination of insignificant model regressors, while preserving the ones which best capture the nonlinear dynamics of the plant, thus rendering the suggested method suitable for identifying multivariable systems, even in the presence of extraneous lags. In order to make the proposed approach compatible with the particular requirements of the identification problem, within the framework of automatic control, the authors have introduced two additional enhancements, namely a dynamic clustering procedure and an adaptive migration mechanism. The performances of the suggested algorithm are revealed by three applications of different complexities: an academic test case featuring an increased number of inputs with time delay and a complex nonlinear industrial plant.