## JMI2012B-8 Symbolic-numeric hybrid optimization for plant/controller integrated design in $\mathcal{H}_\infty$ loop-shaping design (pp.135-140)

Author(s)： Masaaki Kanno and Shinji Hara

J. Math-for-Ind. 4B (2012) 135-140.

Abstract
This paper proposes a plant/controller design integration method for $\mathcal{H}_\infty$ loop-shaping design based on symbolic-numeric hybrid optimization. This approach firstly employs parametric polynomial spectral factorization to accomplish parametric optimization and derive an expression for the optimal cost. Owing to the obtained expression, sensitivity analysis of the achievable performance level with respect to plant parameters is amenable, which allows numerical optimization methods to seek the optimal set of parameter values.

Keyword(s).　 $\mathcal{H}_\infty$ loop-shaping design, plant/controller design integration, symbolic-numeric hybrid optimization, parametric polynomial spectral factorization