非線形微分方程式の数値解法を利用した最大固有値最小化問題の簡単な解法 : 双線形行列不等式に基づくH_∞制御系設計のための基礎的検討(機械力学,計測,自動制御)

概要

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We present a simple numerical method for minimizing the maximum eigenvalues of real-valued symmetric matrices, based on nonlinear differential equation solvers. First, we convert the minimization problem for the maximum eigenvalues, which is nondifferentiable, into a differentiable optimization problem by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for solving the optimization problem. Our method does not require optimization techniques such as the Newton method. Lastly, we demonstrate the effectiveness of the algorithm through some simulation experiments.
一般社団法人日本機械学会の論文
1997-04-25