非线性系统有输入饱和时基于平方和的鲁棒模型预测控制器
Sum of squares-robust model predictive controller for nonlinear system with input saturation

本文针对带有参数不确定和输入饱和的单输入单输出(SISO)仿射非线性系统, 利用反馈线性化, 将非线性 系统转化为带有扰动和状态依赖输入饱和的多胞线性参变(LPV)模型, 进而提出一种基于平方和(SOS)的鲁棒模型 预测控制器(RMPC)设计方法. 基于多胞RMPC控制器, 设计加权状态反馈控制律, 通过引入范数有界定理, 确保扰 动下预测状态收敛到不变集内, 并利用勒让德多项式近似和SOS技术, 将状态依赖输入饱和约束转化为多项式凸优 化问题, 以获得实际和辅助状态反馈律, 所设计的SOS-RMPC控制器能够保证闭环系统的稳定性. 通过与常规多 胞RMPC控制器的仿真比较, 验证了本方法的有效性, 并进一步仿真分析了勒让德多项式阶次对控制器性能的影响.
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.