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

Abstract

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 ($zeta$) 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 the 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. Two cases are considered, noiseless and noisy case which includes an additive white noise to the output measurements. The 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.