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In this paper, we consider an LQR design problem for distributed controlsystems. For large-scale distributed systems, finding a solution might becomputationally demanding due to communications among agents. To this aim, wedeal with LQR minimization problem with a regularization for sparse feedbackmatrix, which can lead to achieve the reduction of the communication links inthe distributed control systems. For this work, we introduce a simple butefficient iterative algorithms - Iterative Shrinkage Thresholding Algorithm(ISTA) and Iterative Sparse Projection Algorithm (ISPA). They can give us atrade-off solution between LQR cost and sparsity level on feedback matrix.Moreover, in order to improve the speed of the proposed algorithms, we designdeep neural network models based on the proposed iterative algorithms.Numerical experiments demonstrate that our algorithms can outperform theprevious methods using the Alternating Direction Method of Multiplier (ADMM)[1] and the Gradient Support Pursuit (GraSP) [2], and their deep neural networkmodels can improve the performance of the proposed algorithms in convergencespeed.

Deep Neural Networks Based on Iterative Thresholding and Projection Algorithms for Sparse LQR Control Design