Proximal Method for $\ell_0-$norm based Sparse Enhanced Control Problems in Large-scale Interconnected Systems
Wah June Leong(leongwjupm.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.
Entry Submitted: 10/08/2019
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