Communications in Information and Systems

Volume 11 (2011)

Number 3

Plant/controller design integration for H2 control based on symbolic-numeric hybrid optimization

Pages: 281 – 306



Hirokazu Anai (Fujitsu Laboratories Ltd, Kawasaki, Japan)

Shinji Hara (Department of Information Physics and Computing, University of Tokyo, Japan)

Masaaki Kanno (Institute of Science and Technology, Niigata University, Japan)


This paper proposes a new plant/controller design integration framework that seeks the optimal pair of the plant and the controller achieving the best possible closed-loop performance in H2 control. The framework is further equipped with a symbolic-numeric hybrid optimization approach to effectively search the optimum. The first step of the suggested approach relies on an algebraic approach to parametric polynomial spectral factorization. The paper first reviews an algebraic approach in the continuous-time case and then generalizes the approach to the δ domain so that the suggested hybrid approach may deal with digital control systems, allowing the sampling period to be treated explicitly as a parameter. Then it is indicated that the optimal cost in the H2 control problem may be characterized in the presence of parameters. It is further discussed that the obtained expression relating the achievable performance level and parameters can be utilized for numerical optimization over the admissible parameter range to find the best parameter values. Two design examples are used to demonstrate the suggested approaches.


parametric polynomial spectral factorization, Gröbner bases, digital control, δ domain, Newton’s method

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