- Proximal Method for $\ell_0-$norm based Sparse Enhanced Control Problems in Large-scale Interconnected Systems Wah June Leong(leongwjupm.edu.my) Changzhi Wu(changzhiwugzhu.edu.cn ) Kok Lay Teo(K.L.Teocurtin.edu.au ) Hong Seng Sim(simhsutar.edu.my ) Abstract: 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. Keywords: Interconnected systems; sparse feedback matrix; $\ell_0-$norm minimization; proximal method; Kurdyka-Lojasiewicz properties. Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Citation: Paper submitted for publication in SIAM Journal of Control and Optimization, 2019. Download: [PDF]Entry Submitted: 10/08/2019Entry Accepted: 10/08/2019Entry Last Modified: 10/08/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.