- 著者
- Tomoyuki Iori Toshiyuki Ohtsuka
- 出版者
- The Operations Research Society of Japan
- 雑誌
- 日本オペレーションズ・リサーチ学会論文誌 (ISSN:04534514)
- 巻号頁・発行日
- vol.63, no.4, pp.114-133, 2020-10-31 (Released:2020-10-31)
- 参考文献数
- 20
This paper proposes a necessary optimality condition derived by a limit operation in projective space for optimization problems of polynomial functions with constraints given as polynomial equations. The proposed condition is more general than the Karush-Kuhn-Tucker (KKT) conditions in the sense that no constraint qualification is required, which means the condition can be viewed as a necessary optimality condition for every minimizer. First, a sequential optimality condition for every minimizer is introduced on the basis of the quadratic penalty function method. To perform a limit operation in the sequential optimality condition, we next introduce the concept of projective space, which can be regarded as a union of Euclidian space and its points at infinity. Through the projective space, the limit operation can be reduced to computing a point of the tangent cone at the origin. Mathematical tools from algebraic geometry were used to compute the set of equations satisfied by all points in the tangent cone, and thus by all minimizers. Examples are provided to clarify the methodology and to demonstrate cases where some local minimizers do not satisfy the KKT conditions.
- 著者
- Taro YANAGIYA Yusuke OKAJIMA Tomoaki HASHIMOTO Toshiyuki OHTSUKA
- 出版者
- The Society of Instrument and Control Engineers
- 雑誌
- SICE Journal of Control, Measurement, and System Integration (ISSN:18824889)
- 巻号頁・発行日
- vol.13, no.5, pp.215-224, 2020 (Released:2020-09-12)
- 参考文献数
- 21
We developed a load frequency control system with stochastic model predictive control (SMPC) for power systems where the market penetration of wind power generation is high. The controller adjusts the electricity price for heat pump water heaters while at the same time controlling thermal power plants and batteries in order to maintain the frequency in the designated range. We propose an approach for solving SMPC problems on Hammerstein models including affine disturbance feedback parametrization. Simulation results show that SMPC with affine disturbance feedback parametrization outperforms both SMPC without parametrization and deterministic model predictive control in terms of the stage-cost and constraint violation.