A Regularized SNPOM for Stable Parameter Estimation of RBF-AR(X) Model

Abstract

Recently, the radial basis function (RBF) network-style coefficients AutoRegressive (with exogenous inputs) [RBF-AR(X)] model identified by the structured nonlinear parameter optimization method (SNPOM) has attracted considerable interest because of its significant performance in nonlinear system modeling. However, this promising technique may occasionally confront the problem that the parameters are divergent in the optimization process, which may be a potential issue ignored by most researchers. In this paper, a regularized SNPOM, together with the regularization parameter detection technique, is presented to estimate the parameters of RBF-AR(X) models. This approach first separates the parameters of an RBF-AR(X) model into a linear parameters set and a nonlinear parameters set, and then combines a gradient-based nonlinear optimization algorithm for estimating the nonlinear parameters and the regularized least squares method for estimating the linear parameters. Several examples demonstrate that the proposed approach is effective to cope with the potential unstable problem in the parameters search process, and may also yield better or similar multistep forecasting accuracy and better robustness than the previous method.

A Two-Stage Scheduling RPC Based on Time-Varying Coefficient Information of State-Dependent ARX Model

“…are optimized by the regularized SNPOM [22]. e details of the regularized SNPOM algorithm can be found in Ref.…”

“…Proof. Substituting the state-space model (11), u(t + j | t) � F(t)X(t + j | t) and (21) into (22), one can get the following inequality:…”

“…where the input voltage U(t) and liquid level H 2 (t) are the input and output, respectively; k α , k (35) are optimized by the R-SNPOM [22]. e detailed optimization process of the nonlinear parameters and linear parameters can be found in Ref.…”

“…e SD-ARX model is a quasi-LPV model with functional coefficients and is often used in nonlinear system modeling [20]. Using RBF to approximate the state-dependent coefficients of the SD-ARX model generates the RBF-ARX model [21,22]. ese type model-based MPC strategies have been successfully applied to many systems, such as the industrial drying process [23,24], the NOx decomposition process [21,25], the water tank system [26], and the ship's tracking control [27].…”

“…ese type model-based MPC strategies have been successfully applied to many systems, such as the industrial drying process [23,24], the NOx decomposition process [21,25], the water tank system [26], and the ship's tracking control [27]. But, most of these literatures [21][22][23][24][25][26] are limited to nominal conditions, and the stabilities of these MPCs are also difficult to guarantee.…”