Multilinear model predictive control is a strategy to track various set-points in a nonlinear process with a wide operating region, because it can predict the dynamic behavior of a part of the operating region using a linear model or weighted summation of linear models. In addition, it is computationally efficient compared to nonlinear model predictive control. The gap metric is exploited to evaluate the weights of linear models at each sampling time. In this work, we propose the design of local controllers for different operating regions using the gap metric, and prove that each local controller has the offset-free tracking property in the corresponding part of the operating region. We also construct a graph to find the optimal path from an initial point to a set-point and propose a switching strategy using the local controllers and the optimal path. It is proved that the resulting global controller can steer the state to anywhere in the operating region. A continuous stirred tank reactor process is studied to demonstrate the effectiveness of the proposed algorithms. Simulation studies show that the controllers designed by the proposed algorithm achieve the offset-tracking property when the initial point and the set-point are randomly chosen in the operating region.

多线性模型预测控制是一种在具有宽工作区域的非线性过程中跟踪各种设定点的策略，因为它可以使用线性模型或线性模型的加权求和来预测部分工作区域的动态行为。此外，与非线性模型预测控制相比，它的计算效率很高。利用差距度量来评估每个采样时间的线性模型的权重。在这项工作中，我们建议使用间隙度量设计不同操作区域的本地控制器，并证明每个本地控制器在操作区域的相应部分均具有无偏移跟踪特性。我们还构造了一个图，以找到从初始点到设定点的最佳路径，并提出了使用本地控制器和最佳路径的切换策略。事实证明，最终的全局控制器可以将状态引导到操作区域中的任何位置。研究了连续搅拌釜反应器过程，以证明所提出算法的有效性。仿真研究表明，当在工作区域中随机选择初始点和设定点时，该算法设计的控制器具有偏移跟踪特性。