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Mathematical Problems in Engineering
Volume 2014, Article ID 906717, 8 pages
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.


Control of complex systems is one of the fundamental problems in control theory. In this paper, a control method for complex systems modeled by a probabilistic Boolean network (PBN) is studied. A PBN is widely used as a model of complex systems such as gene regulatory networks. For a PBN, the structural control problem is newly formulated. In this problem, a discrete probability distribution appeared in a PBN is controlled by the continuous-valued input. For this problem, an approximate solution method using a matrix-based representation for a PBN is proposed. Then, the problem is approximated by a linear programming problem. Furthermore, the proposed method is applied to design of real-time pricing systems of electricity. Electricity conservation is achieved by appropriately determining the electricity price over time. The effectiveness of the proposed method is presented by a numerical example on real-time pricing systems.