This paper considers linear quadratic optimal control problem of large-scale interconnected systems. An algorithmic framework is constructed to design controllers that provide a desired tradeoff between the system performance and the sparsity of the static feedback matrix. This is accomplished by introducing a minimization problem involving $\ell_0-$norm of the feedback matrix subject to a maximum allowable compromise in performance. To address the computational difficulty caused by the use of $\ell_0-$norm, we propose to approximate the $\ell_0-$norm by its Moreau envelope and the proximal algorithm with extrapolation is constructed to solve the approximated optimization problem. Convergence analysis based on the Kurdyka-Lojasiewicz (KL) properties is presented. Our numerical examples show that the proposed framework can obtain feedback matrices with higher sparsity when compared with the model based on the $\ell_1-$norm relaxation.
Paper submitted for publication in SIAM Journal of Control and Optimization, 2019.
View Proximal Method for $ell_0- based Sparse Enhanced Control Problems in Large-scale Interconnected Systems