A quadratic entropy algorithm for efficient online identification of LPV-ARX models using LS-SVM

Modeling non-linear systems has always been a challenge in the field of control engineering. Linear Parameter Varying (LPV) models can be a valid choice to model complex systems, since they have a simple linear structure, but time varying coefficients that captures the system dynamics according to a scheduling signal measured from the system. A common approach to identify a LPV system in an ARX form is the Least Squares Support Vector Machines (LS-SVM) method. However, due to its computational complexity, it is difficult to employ such algorithm in online applications, when a model must be identified each time a new datum is collected from the system. An efficient recursive update algorithm has been recently presented in the literature for such cases, where only the most informative data points are selected to update the model, thus generally reducing the required computational effort. However, in certain conditions such algorithm selects too many data points, still leading to an high computational time. In this work, a quadratic entropy based algorithm is proposed to overcome the limitations found in the literature, providing a better trade-of between identification accuracy and computational time.