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Mathematical Problems in Engineering
Volume 2014, Article ID 906717, 8 pages
http://dx.doi.org/10.1155/2014/906717
Research Article

A Probabilistic Approach to Control of Complex Systems and Its Application to Real-Time Pricing

School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 16 July 2014; Accepted 1 September 2014; Published 17 September 2014

Academic Editor: Rajan Rakkiyappan

Copyright © 2014 Koichi Kobayashi and Kunihiko Hiraishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Tabuada, Verification and Control of Hybrid Systems, Springer, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. M. Adomi, Y. Shikauchi, and S. Ishii, “Hidden Markov model for human decision process in a partially observable environment,” in Proceedings of the 20th International Conference on Artificial Neural Networks, vol. 6353 of Lecture Notes in Computer Science, pp. 94–103, 2010.
  3. H. De Jong, “Modeling and simulation of genetic regulatory systems: a literature review,” Journal of Computational Biology, vol. 9, no. 1, pp. 67–103, 2002. View at Publisher · View at Google Scholar · View at Scopus
  4. S. A. Kauffman, “Metabolic stability and epigenesis in randomly constructed genetic nets,” Journal of Theoretical Biology, vol. 22, no. 3, pp. 437–467, 1969. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Mochizuki, “An analytical study of the number of steady states in gene regulatory networks,” Journal of Theoretical Biology, vol. 236, no. 3, pp. 291–310, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, “Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks,” Bioinformatics, vol. 18, no. 2, pp. 261–274, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. B. Faryabi, G. Vahedi, J.-F. Chamberland, A. Datta, and E. R. Dougherty, “Intervention in context-sensitive probabilistic boolean networks revisited,” Eurasip Journal on Bioinformatics and Systems Biology, vol. 2009, Article ID 360864, 13 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Pal, A. Datta, M. L. Bittner, and E. R. Dougherty, “Intervention in context-sensitive probabilistic Boolean networks,” Bioinformatics, vol. 21, no. 7, pp. 1211–1218, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. K. Kobayashi and K. Hiraishi, “Optimal control of gene regulatory networks with effectiveness of multiple drugs: a boolean network approach,” BioMed Research International, vol. 2013, Article ID 246761, 11 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. I. Shmulevich, E. R. Dougherty, and W. Zhang, “Control of stationary behavior in probabilistic Boolean networks by means of structural intervention,” Journal of Biological Systems, vol. 10, no. 4, pp. 431–445, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. Y. Xiao and E. R. Dougherty, “The impact of function perturbations in Boolean networks,” Bioinformatics, vol. 23, no. 10, pp. 1265–1273, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Kobayashi and K. Hiraishi, “Design of boolean networks based on prescribed singleton attractors,” in Proceedings of the European Control Conference, pp. 1504–1509, 2014.
  13. S. Borenstein, M. Jaske, and A. Rosenfeld, Dynamic Pricing, Advanced Metering, and Demand Response in Electricity Markets, Center for the Study of Energy Markets, University of California, Berkeley, Calif, USA, 2002.
  14. M. Roozbehani, M. Dahleh, and S. Mitter, “On the stability of wholesale electricity markets under real-time pricing,” in Proceedings of the 49th IEEE Conference on Decision and Control (CDC '10), pp. 1911–1918, December 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. A.-H. Mohsenian-Rad, V. W. S. Wong, J. Jatskevich, and R. Schober, “Optimal and autonomous incentive-based energy consumption scheduling algorithm for smart grid,” in Proceedings of the Innovative Smart Grid Technologies (ISGT '10), pp. 1–10, Gaithersburg, Md, USA, January 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. C. Vivekananthan, Y. Mishra, and G. Ledwich, “A novel real time pricing scheme for demand response in residential distribution systems,” in Proceedings of the 39th Annual Conference of the IEEE Industrial Electronics Society (IECON '13), pp. 1956–1961, Vienna, Austria, November 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Kobayashi and K. Hiraishi, “Optimal control of probabilistic Boolean networks using polynomial optimization,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E95-A, no. 9, pp. 1512–1517, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. D. Cheng and H. Qi, “Controllability and observability of Boolean control networks,” Automatica, vol. 45, no. 7, pp. 1659–1667, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. D. Cheng, H. Qi, and Z. Li, Analysis and Control of Boolean Network: A Semi-Tensor Product Approach, Communications and Control Engineering Series, Springer, London, UK, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. E. F. Camacho and C. B. Alba, Model Predictive Control, Springer, 2nd edition, 2007.
  21. SparsePOP, http://www.is.titech.ac.jp/~kojima/SparsePOP/SparsePOP.html.