This article presents an alternating direction method of multipliers (ADMM) algorithm for solving large‐scale model predictive control (MPC) problems that are invariant under the symmetric‐group. Symmetry was used to find transformations of the inputs, states, and constraints of the MPC problem that decompose the dynamics and cost. We prove an important property of the symmetric decomposition for the symmetric‐group that allows us to efficiently transform between the original and decomposed symmetric domains. This allows us to solve different subproblems of a baseline ADMM algorithm in different domains where the computations are less expensive. This reduces the computational cost of each iteration from quadratic to linear in the number of repetitions in the system. In addition, we show that the memory complexity for our ADMM algorithm is also linear in number of repetitions in the system, rather than the typical quadratic complexity. We demonstrate our algorithm for two case studies; battery balancing and heating, ventilation, and air conditioning. In both case studies, the symmetric algorithm reduced the computation‐time from minutes to seconds and memory usage from tens of megabytes to tens or hundreds of kilobytes, allowing the previously nonviable MPCs to be implemented in real time on embedded computers with limited computational and memory resources.

中文翻译：

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对称模型预测控制的乘数算法交替方向法

本文提出了一种乘方交替方向方法（ADMM），用于解决在对称组下不变的大规模模型预测控制（MPC）问题。对称性用于查找分解动力和成本的MPC问题的输入，状态和约束的变换。我们证明了对称组对称分解的重要属性，它使我们能够在原始对称域和分解的对称域之间进行有效转换。这使我们能够在计算成本较低的不同领域中解决基准ADMM算法的不同子问题。这将系统中重复次数的每次迭代的计算成本从二次降低为线性。此外，我们表明，ADMM算法的内存复杂度在系统中的重复次数上也是线性的，而不是典型的二次复杂度。我们针对两个案例演示了我们的算法；电池平衡以及加热，通风和空调。在这两个案例研究中，对称算法将计算时间从几分钟减少到几秒钟，并将内存使用量从数十兆字节减少到数十或数百千字节，从而使以前不可行的MPC可以在计算和内存有限的嵌入式计算机上实时实现。资源。