用外包集逼近预测控制的最大终端状态集

Using enclosing sets to approach the maximal terminal state region in model predictive control

为了增大模型预测控制的终端状态集,设计了一种迭代逼近法,得到了一个最大终端状态集的外包集序列从理论上证明了当迭代次数趋于无穷步时,此外包集序列逐渐收敛至最大终端状态集.此序列中的外包集,采用支持向量机作为分类工具依次从状态空间中分离得到.设计了一个基于阈值的终止函数,当前后两个外包集满足终止条件时,终止迭代,并将后面的一个外包集作为终端状态集的估计,阈值越小,迭代次数越大,此外包集对最大终端状态集的逼近精度越高.最后,将此终端状态集估计应用于预测控制,仿真结果验证了本文方法的可行性.

To enlarge the terminal state region of the model predictive control（MPC）, we design an iterative method and obtain an enclosing sets sequence for the maximal terminal state region. We prove that, when the iteration step goes to infinity, the enclosing sets sequence converges to the maximal terminal state region. The enclosing sets in the sequence are extracted one by one from the state space by using support vector machine（SVM） classifier. A stop-function based on a threshold is designed. When two consecutive enclosing sets satisfy the stop condition, the iteration will be terminated and the latter one will be considered the estimated terminal state region. The smaller the threshold, the greater the iteration times and the higher the precision of this enclosing set approaching to the maximal terminal state region will be. Finally, the estimated terminal state region is applied to MPC and the simulation results show the feasibility of the method proposed in this paper.