Solving large-scale optimization problems with numerous constraints and optimization variables is a challenging task. Partial explicit MPC enables solving the large-scale optimization problem efficiently. This paper pushes the idea of partial explicit MPC to the fixed complexity parametric solution. The idea is to replace the polytopic critical regions that have a variable number of halfspaces with the maximal volume inner approximation based on the Chebyshev balls. As the approximation has a fixed and known structure, the memory footprint of the parametric solution is also fixed and known in advance, without the necessity to solve the large-scale optimization problem. This valuable property enables scaling the solution size a priori to meet the requirements of the hardware, where the MPC controller will be installed. The proposed method also dramatically reduced the memory burden of the partial explicit solution. Moreover, the proposed method improves the accuracy of the initialization of the hot-start procedure.

解决具有众多约束和优化变量的大规模优化问题是一项具有挑战性的任务。部分显式 MPC 能够有效地解决大规模优化问题。本文将部分显式 MPC 的思想推到了固定复杂度的参数解中。这个想法是用基于切比雪夫球的最大体积内部近似替换具有可变数量的半空间的多面体临界区域。由于近似具有固定且已知的结构，因此参数解的内存占用也是固定且预先已知的，无需求解大规模优化问题。这一宝贵的特性可以预先扩展解决方案的大小，以满足将安装 MPC 控制器的硬件要求。所提出的方法还大大减少了部分显式解决方案的内存负担。此外，所提出的方法提高了热启动程序初始化的准确性。