Optimal control for discrete and continuous stochastic descriptor systems with application to a factory management model

Abstract

In this paper, optimal control models ruled by discrete and continuous stochastic descriptor systems are investigated in order. These descriptor systems are assumed to be regular and impulse-free. For settling discrete optimal control problems, a recurrence equation is proposed with the help of dynamic programming method. Then, optimal control problems for two types of discrete stochastic descriptor systems are considered and optimal solutions are presented by analytical expressions. To simplify continuous optimal control problems, an equation of optimality is derived according to the principle of optimality, and it reveals the essential connection between optimal value and optimal control. Two numerical examples and a factory management model are provided to illustrate the validness of above results.

Keywords:

• Optimal control
• stochastic descriptor systems
• dynamic programming method
• recurrence equation
• equation of optimality

Disclosure statement

No potential conflict of interest is reported by the authors.

Additional information

Funding

This work is supported by the Natural Science Foundation of Jiangsu Province [grant number BK20210633] and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China [grant number 21KJB120008].