Optimal control using microscopic models for a pollutant elimination problem

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• 作者：Yuecheng Yang ; Xiaoming Hu
• 关键词：Moments ; multi ; agent system ; optimal control ; partial differential equation
• 刊名：Journal of Systems Science and Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：30
• 期：1
• 页码：86-100
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Operation Research/Decision Theory; Mathematics of Computing; Complex Systems; Statistics, general;
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences
• ISSN：1559-7067
• 卷排序：30

文摘

Optimal control problem with partial derivative equation (PDE) constraint is a numerical-wise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman (HJB) equation approximation. For solving the problem, only an HJB equation (a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.