基于多面体可达集的时间最优模型预测控制

Time optimal model predictive control based on polyhedral reachable set

针对有界状态干扰下的线性时变系统,提出一种新的时间最优模型预测控制算法.在离线情况下通过求解一系列的线性优化问题确定次优的多面体N步可达集,根据这些可达集在线优化计算得到的输入量使系统状态尽快收敛到稳定区域.离线求解多面体可达集的方法可处理非对称约束,相比于以往的方法避免了在N增加时顶点数可能呈指数增多的问题,同时省去了过多复杂的多面体间的运算,因而便于在实际问题中应用.

A new time optimal model predictive control paradigm is proposed for the linear time-varying system with bounded state disturbance. The suboptimal polyhedral N-step reachable sets are determined offline by solving a series of linear programs, and then the inputs are optimized online to render the states into the terminal set as fast as possible. This method can handle asymmetric constraints. Compared with previous methods, it avoids the possibility that the number of vertices increases exponentially with the step N, and thus eliminates excessive complex polytope operations. The results show that the proposed approach is convenient for practical purposes.