最大控制律的多面体不变集鲁棒模型预测控制

Robust Model Predictive Control Based on Polyhedral Invariant Sets with Maximum Control Laws

为实现线性变参数系统的快速稳定控制,提出一种最大控制律的多面体不变集鲁棒模型预测控制算法。离线时,通过设定一组渐近趋向于稳定点的给定值,按照状态变量到稳定点距离大致相同的原则,构建一系列状态变量值集合,通过优化得到每个集合中较大的控制律,然后采用反推的方式优化得到一系列最大的控制律,并结合系统的输入输出约束得到离线多面体不变集。在线时,根据每个采样周期状态变量在多面体不变集中的位置,通过线性插值优化得到系统的实际控制律。给出离线在线算法的详细步骤和系统的闭环稳定性证明。通过仿真比较验证所提算法的有效性,表明所提算法使系统响应更为快速和稳定。

In order to realize fast and stable control of the linear variable parameter system a robust model predictive control algorithm based on polyhedral invariant sets with maximum control laws is proposed.When offline by setting a group of progressive values approaching the stable point according to the principle that the distance from the state variable to the stable point is roughly the same a sequence of state variable sets is constructed and the larger control law in each set is obtained through optimization.The laws are then optimized in a backstepping way to obtain a series of maximum control laws,and are combined with the input and output constraints of the system to obtain the offline polyhedral invariant sets.When online the actual control law of the system is obtained by linear interpolation optimization according to the position of state variables of each sampling period in the polyhedron invariant sets.The detailed steps of the offline and online algorithms and the closed-loop stability proof of the system are given.The simulation results prove the effectiveness of the proposed algorithm and indicate that the proposed algorithm makes the closed-loop response of the system more rapid and stable.