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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 952310, 10 pages
Research Article

Optimal Control of Probabilistic Logic Networks and Its Application to Real-Time Pricing of Electricity

1Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan
2School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 1 July 2015; Revised 18 October 2015; Accepted 16 November 2015

Academic Editor: Qingling Zhang

Copyright © 2015 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.


In analysis and control of large-scale complex systems, a discrete model plays an important role. In this paper, a probabilistic logic network (PLN) is considered as a discrete model. A PLN is a mathematical model where multivalued logic functions are randomly switched. For a PLN with two kinds of control inputs, the optimal control problem is formulated, and an approximate solution method for this problem is proposed. In the proposed method, using a matrix-based representation for a PLN, this problem is approximated by a mixed integer linear programming problem. In application, real-time pricing of electricity is studied. In real-time pricing, electricity conservation is achieved by setting a high electricity price. A numerical example is presented to show the effectiveness of the proposed method.