Enhanced Particle Swarm Optimisation Algorithms for Multiple-input Multiple-output System Modelling Using Convolved Gaussian Process Models

Abstract

Convolved Gaussian process (CGP) can capture the input-output correlation, and the correlation of multiple outputs. This is beneficial to the modelling problem of multiple-input multiple-output (MIMO) systems. One key issue of CGP is the learning of hyperparameters from input-output observations. This is typically performed by maximising the log-likelihood (LL) function using gradient based approaches. However, the LL value is not a reliable indicator for judging the quality of intermediate models. We address this issue by minimising the model output error instead. In addition, three enhanced particle swarm optimisation (PSO) algorithms are proposed to solve the optimisation problem because gradient based approaches often get stuck in local optima. The simulation results on numerical linear and nonlinear systems demonstrate the effectiveness of minimising the model output error to learn hyperparameters, and the better performance of using enhanced PSOs compared to gradient based approaches.