State Space LS-SVM for Polynomial Nonlinear State Space Model Based Generalized Predictive Control of Nonlinear Systems

摘要

This paper proposes a novel state space least squares support vector machine (SS LS-SVM) for polynomial nonlinear state space (PNLSS) model based recursive system identification. SS LS-SVM, which also possesses an adaptive kernel function, provides an optimum formulation of the monomials ( ζ) of the states and input in the PNLSS model. Hence, the PNLSS model encompasses the proposed SS LS-SVM. Recursive nonlinear state space identification is developed in the output error prediction context. The input-output observations are processed sequentially, hence leading to recursive update of the parameters using conventional Gauss-Newton optimization. System states do not need to be measured. However, to to yield a conformal representation of the actual system, number of states need to be known via some physical insight. This characterizes the identification procedure as a grey box one. The PNLSS model is employed in the generalized predictive control (GPC) of a nonlinear continuously stirred tank reactor (CSTR) system. The case which includes additive white noise on the output measurements and a time-varying parameter in the nonlinear system is considered. Numerical applications give the results of a high closed loop identification performance addition to the smooth control input and closely tracking the reference in the GPC scheme.