Stable predictive control based on Toeplitz equation and LS-SVM

A stable predictive controller (SPC) based on least squares support machine(LS-SVM) model and Toeplitz predictive equation is presented. For a given controlled plant, the system model is bulit by LS-SVM method. After the achieved system model is transformed into linear input-output equation, the Toeplitz equation can be introduced to predict dynamic behavior in the future. The optimal control law can be obtained by calculating the derivative of the objective function to an intermediate vector. The condition for closed-loop system stability is given and proved completely. The simulation is implemented in a open-loop unstable system with unknown order and delay time, and the results reveals the effectiveness and merit of the presented algorithms.