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

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.