The Pareto Optimal Control of Bilinear Stochastic Systems

In complex industrial big-data systems, bilinear stochastic systems have the ability to provide accurate industrial process modeling, precise control, optimization and decision support. Bilinear stochastic systems can provide effective solutions for the intelligence and optimization of industrial processes, thus achieving precise control and stable operation. In this paper, a bilinear stochastic system based on multi-player in finite horizon is investigated. The Pareto cooperative game problem can be solved by applying a weighted sum approach for the objective function of each player. Firstly, we obtain the Pareto-optimal control strategy for the system under the consideration of the indefinite objective function. Secondly, because of the difficulty of solving the Hamilton-Jacobi equation (HJE), the obtained control strategy is represented according to the method of tensor power series expansion. Thirdly, we obtain all Pareto solutions and the Pareto frontier. Finally, a simulation example is provided to illustrate the accuracy of the theory.