The piecewise parametric optimal control of uncertain linear quadratic models

ABSTRACT

The optimal control of linear quadratic model is given in a feedback form and determined by the solution of a Riccati equation. However, the control-related Riccati equation usually cannot be solved analytically such that the form of optimal control will become more complex. In this paper, we consider a piecewise parametric optimal control problem of uncertain linear quadratic model for simplifying the form of optimal control. By introducing a piecewise control parameter, a piecewise parametric optimal control model is established. Then we present a parametric optimisation method for solving the optimal piecewise control parameter. Finally, an uncertain inventory-promotion optimal control problem is discussed and a comparison is made to show the effectiveness of proposed piecewise parametric optimal control model.

KEYWORDS:

• Optimal control
• uncertain linear quadratic model
• parametric optimisation
• piecewise control parameter

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Yuanguo Zhu http://orcid.org/0000-0003-3176-4428

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 61673011) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 18KJB110012).

Notes on contributors

Bo Li

Bo Li received the Ph.D. degree in mathematics from Nanjing University of Science and Technology, Nanjing, China, in 2017. He is currently a lecturer with the School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, China. His research interests include optimal control, uncertain differential equation, and uncertain portfolio selection.

Yuanguo Zhu

Yuanguo Zhu received the Ph.D. degree in mathematics from Tsinghua University, Beijing, China, in 2004. He is currently a professor with the School of Science, Nanjing University of Science and Technology, Nanjing, China. His research interests include optimal control, optimization, and intelligent computing.