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

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