Selective recursive kernel learning for online identification of nonlinear systems with NARX form

Online identification of nonlinear systems is still an important while difficult task in practice. A general and simple online identification method, namely Selective Recursive Kernel Learning (SRKL), is proposed for multi-input–multi-output (MIMO) systems with the nonlinear autoregressive with exogenous input form. A two-stage RKL online identification framework is first formulated, where the information contained by a sample (i.e., the new arriving or old useless one) can be introduced into and/or deleted from the model, recursively. Then, a sparsification strategy to restrict the model complexity is developed to guarantee all the output channels of the MIMO model accurate simultaneously. Specially, a novel pruning approach based on the fast leave-one-out cross-validation criterion is explored to acquire generalization ability by determining and then deleting the useless information. Consequently, the model can adaptively adjust its structure to capture the process dynamics. The SRKL method is applied intensively to several nonlinear systems for multifold identification aims. The obtained results show that SRKL is superior to traditional methods, e.g., artificial neural networks and fuzzy systems, in different situations. The benefits of its accuracy, reliable performance and simple implementation in practice indicate that SRKL is promising for online identification of nonlinear systems.