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

• Main Authors: Koichi Kobayashi, Kunihiko Hiraishi
• Format: Article
• Language: English
• Published: Hindawi Limited 2014-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2014/906717

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.