Abstract:

For a class of linear variable parameter systems with input and output constraints, a robust model predictive control algorithm based on polyhedral invariant sets with variable polytope structure is proposed. The proposed algorithm is divided into the online part and the offline part. The offline algorithm constructs the unknown but bounded error description model of the system, and obtains the variable parameters polytope structures according to the change of state, than converts it into the polytope form of the state space model.A series of offline nested polyhedral invariant sets are obtained by using the optimization method of linear matrix inequality. Based on the position of the state variable in the polyhedral invariant sets sequence and considering the change of polytope structure, the online algorithm gets the actual control laws of the system through the linear interpolation optimization. The detailed steps of the algorithm and the closed-loop stability proof of the system are given. The simulation results verify the effectiveness of the algorithm and show that the algorithm makes the closed-loop response of the system faster and more stable.

Key words: linear variable parameter system, robust model predictive control, polytope, polyhedral invariant sets

摘要：

针对一类具有输入输出约束的线性变参数系统，提出了一种可变多胞体结构的多面体不变集鲁棒模型预测控制算法，算法分为在线和离线两个部分。离线算法构建系统的未知但有界误差描述模型，根据状态的变化得到可变参数的多胞体结构，并转化为状态空间模型的多胞体形式，然后采用线性矩阵不等式的优化方式得到一系列离线嵌套多面体不变集。在线算法根据状态变量在嵌套多面体不变集中的位置，结合可变多胞体结构，通过线性插值的优化方式得到系统的实际控制律。给出算法的详细步骤和系统闭环稳定性证明。仿真结果验证了该算法的有效性，表明该算法使系统的闭环响应更为快速和稳定。

关键词: 线性变参数系统, 鲁棒模型预测控制, 多胞体, 多面体不变集