Nagahara, M.; Iwai, Y.; Sebe, N. Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design. Algorithms2022, 15, 322.
Nagahara, M.; Iwai, Y.; Sebe, N. Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design. Algorithms 2022, 15, 322.
Nagahara, M.; Iwai, Y.; Sebe, N. Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design. Algorithms2022, 15, 322.
Nagahara, M.; Iwai, Y.; Sebe, N. Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design. Algorithms 2022, 15, 322.
Abstract
In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is NP-hard. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library.
Copyright:
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