An analysis of hot‐started ADMM for linear MPC
An analysis of hot‐started ADMM for linear MPC
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DOI：
10.1049/cth2.12174
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发表时间：
2021-08
影响因子：
2.6
通讯作者：
Mitsuru Toyoda;Mirai Tanaka
中科院分区：
文献类型：
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作者：
Mitsuru Toyoda;Mirai Tanaka
研究了带正则项的线性模型预测控制问题的交替方向乘子法（ADMM）的收敛性。与传统的结果相比，本文重点研究了ADMM的动力学结构，推导了ADMM动力学状态变量的线性收敛性。在与MPC问题相关的在线优化问题中，由于计算时间是一个重要问题，热启动技术被广泛采用，其中算法的初始点被设置为先前优化问题的收敛点，以改善收敛性在这里，通过利用所提出的收敛性分析框架，探索热启动的有效性，并推导出迭代次数的上界，以保证所获得的迭代解的所需精度。提出的热启动框架导出了MPC问题中ADMM惩罚参数的选择准则，并促进了有效的迭代，数值算例验证了这一点。
A convergence analysis of the alternating direction method of multipliers (ADMM) for linear model predictive control (MPC) problems with regularization terms is addressed here. Compared with conventional results, this paper focuses on the dynamical structure of the ADMM and derives the linear convergence of the state variables of the ADMM dynamics.In on‐line optimization problems associated with MPC problems, because the computation time is a significant issue, a hot‐start technique in which an initial point of the algorithm is set as the convergence point for the previous optimization problem is widely employed to improve the convergence property. Here, by utilizing the proposed convergence analysis framework, the effectiveness of the hot‐start is explored, and the upper bounds of the number of iterations to guarantee the required accuracy of an obtained iterative solution are deduced. The proposed hot‐start framework derives a criterion for choosing the penalty parameter of the ADMM in MPC problems and facilitates effective iteration, which is validated in a numerical example.