【摘要】 基于显式PWA(piece-wise affine)模型和Lyapunov函数,提出了一种模型预测控制系统的低保守稳定性分析方法。通过在PWA模型的状态分区上,寻找分段二次Lyapunov函数,把闭环预测控制系统的稳定性分析问题转化为线性矩阵不等式(linear matrix inequality,LMI)问题,并应用现有的高效凸规划算法来求解。对PWA模型的状态区域进一步的细化凸划分,以增加找到分段二次Lyapunov函数的可能性,减低闭环系统稳定性分析的保守性。数值仿真计算表明该方法是可行有效的。更多还原

【Abstract】 A piece-wise affine (PWA) model of a closed-loop model predictive control (MPC) system and Lyapunov functions are used for a stability analysis of a less conservative closed loop MPC system.A piece-wise quadratic Lyapunov function is used over the entire state region to transform the stability of the closed-loop MPC system into a linear matrix inequality problem,which can be efficiently solved using available convex programming algorithms.Further convex partitioning of the state’s regions increases the possibility of finding the piece-wise quadratic Lyapunov functions,which reduces the conservativeness of the stability analysis.Numerical simulations show the effectiveness of this approach.更多还原