A Kernel-based Approach to MIMO LPV State-space Identification and Application to a Nonlinear Process System

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This paper first describes the development of a nonparametric identification method for linear parameter-varying (LPV) state-space models and then applies it to a nonlinear process system. The proposed method uses kernel-based least-squares support vector machines (LS-SVM). While parametric identification methods require proper selection of basis functions in order to avoid over-parametrization or structural bias, the problem of variance-bias tradeoff is avoided by estimating the functional dependencies of the state-space representation on the LPV scheduling variables using measured input and output data under the LS-SVM framework. The proposed formulation allows for LS-SVM to reconstruct and uncover static, as well as dynamic dependencies on scheduling variables in multi-input multi-output (MIMO) LPV models. This is achieved by assuming that the states are measurable, which is a common scenario during online control of many chemical processes described by lumped parameter models. The proposed method does not require an explicit declaration of the feature maps of the nonlinearities of the assumed model structure; instead, it requires the selection of a nonlinear kernel function and tuning its parameters. The developed identification method is applied to a continuous stirred tank reactor (CSTR) model under realistic noise conditions. Another numerical example along with the CSTR system illustrates the performance of the proposed algorithm under both static and dynamic dependence on the scheduling variables.