Sum of squares-robust model predictive controller for nonlinear system with input saturation
HU Chao-fang
XIE Qian-qian
Abstract：For the single-input-single-output (SISO) affine nonlinear system subject to uncertain parameters and input saturation, we use the feedback linearization method to build a polytopic linear parameter-varying (LPV) model with disturbance and state-dependent input saturation, and develop a robust model predictive controller (RMPC) based on the sum-of-squares (SOS) method. On the basis of this polytopic RMPC, we design the weighted state-feedback control law. The norm-bounded theorem is introduced to guarantee predictive states with disturbance to converge to the invariant set. Moreover, the restrictive condition of state-dependent input saturation is transformed to the polynomial convex optimization problem by using the Legendre polynomial approximation and SOS technique. Then, the actual and auxiliary feedback laws are obtained. The stability of the closed-loop system is guaranteed by the designed SOS-RMPC controller. Simulation results demonstrate the effectiveness and superiority of the proposed method over the traditional polytopic LPV-RMPC controller. The effect of the order of Legendre polynomial on the control performance is also investigated by simulations.
Keywords：model predictive controlinput saturationlinear parameter-varying modelfeedback linearizationsum of squares
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：8( 321-328 )