论文标题
迭代阈值和投影算法和基于模型的深神经网络，用于稀疏LQR控制设计
Iterative Thresholding and Projection Algorithms and Model-Based Deep Neural Networks for Sparse LQR Control Design
论文作者
论文摘要
在本文中，我们考虑了分布式控制系统的LQR设计问题。对于大型分布式系统，由于代理之间的通信，找到解决方案可能是计算要求的。为此，我们处理了稀疏反馈矩阵的正规化解决LQR最小化问题，这可以导致降低分布式控制系统中的通信链接。对于这项工作，我们引入了简单但有效的迭代算法 - 迭代收缩阈值算法（ISTA）和迭代稀疏投影算法（ISPA）。他们可以在反馈矩阵上为我们提供LQR成本和稀疏水平之间的权衡解决方案。此外，为了提高所提出算法的速度，我们根据提出的迭代算法设计深神经网络模型。数值实验表明，我们的算法可以使用乘数的交替方向方法（ADMM）[2]和梯度支持Pursuit（GRASP）[3]胜过先前的方法，并且其深层神经网络模型可以提高拟议算法在融合速度中所提出的算法的性能。
In this paper, we consider an LQR design problem for distributed control systems. For large-scale distributed systems, finding a solution might be computationally demanding due to communications among agents. To this aim, we deal with LQR minimization problem with a regularization for sparse feedback matrix, which can lead to achieve the reduction of the communication links in the distributed control systems. For this work, we introduce simple but efficient iterative algorithms -- Iterative Shrinkage Thresholding Algorithm (ISTA) and Iterative Sparse Projection Algorithm (ISPA). They can give us a trade-off solution between LQR cost and sparsity level on feedback matrix. Moreover, in order to improve the speed of the proposed algorithms, we design deep neural network models based on the proposed iterative algorithms. Numerical experiments demonstrate that our algorithms can outperform the previous methods using the Alternating Direction Method of Multiplier (ADMM) [2] and the Gradient Support Pursuit (GraSP) [3], and their deep neural network models can improve the performance of the proposed algorithms in convergence speed.
