In this paper, a subdivision strategy for the adjoining cell mapping method to solve the global optimal control problems for multi-input-multi-output systems is proposed. The subdivision strategy constructs the discrete optimal control table first by a rough discretization of the state space, which can identify uncontrollable regions. Then the optimal feedback control from the selected initial state is instituted. The rough cells where the feedback control trajectory crosses are subdivided into smaller cells and the finer discrete optimal control table is obtained after the second search. The further discretization of the target cell and control inputs can further enhance the terminate control precision. The calculation can also take the advantage of GPU parallel technology that will greatly enhance the computation efficiency. Two examples illustrate the feasibility and validity of the subdivision strategy to solve optimal control problems for multi-input-multi-output systems. The proposed method offers an efficient alternative numerical way to obtain the approximate optimal control solution with global optimum for nonlinear multi-input-multi-output systems.

中文翻译：

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多输入多输出系统全局最优控制下邻接单元映射的细分策略

本文提出了一种求解多输入多输出系统全局最优控制问题的邻接单元映射方法的细分策略。细分策略首先通过状态空间的粗略离散化构造离散最优控制表，可以识别不可控区域。然后从选定的初始状态开始最佳反馈控制。将反馈控制轨迹交叉的粗糙单元格细分为更小的单元格，经过二次搜索得到更精细的离散最优控制表。目标单元和控制输入的进一步离散化可以进一步提高终止控制的精度。计算还可以利用GPU并行技术，大大提高计算效率。两个例子说明了细分策略解决多输入多输出系统最优控制问题的可行性和有效性。所提出的方法提供了一种有效的替代数值方法来获得非线性多输入多输出系统全局最优的近似最优控制解。