Two‐person games for uncertain random singular dynamic systems

• Published in: IET control theory & applications Vol. 17; no. 5; pp. 542 - 558
• Main Authors: Chen, Xin, Zhu, Yuanguo, Park, Ju H.
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01.03.2023
• Subjects: Complex systems; control system analysis; Difference equations; discrete time systems; dynamic programming; Dynamical systems; Equilibrium; Euclidean space; Game theory; Games; Random variables; Subject specialists
• DOI: 10.1049/cth2.12400
• ISSN: 1751-8644

A complex system exhibiting uncertainty as well as randomness may be portrayed by an uncertain random singular difference equation. This paper investigates two‐person nonzero‐sum and zero‐sum games based on uncertain random singular difference equations. First, an approach is proposed to translate the two‐person nonzero‐sum game into an equivalent game for a standard uncertain random dynamic system. The relevant recursive equations are developed to search the Nash equilibrium for the converted game. Solving the related recursive equations yields the solution to such a game. Following that, a Max‐Min Theorem is provided for finding the saddle‐point equilibrium of an uncertain random two‐person zero‐sum game. Finally, a numerical example is offered to demonstrate the validity of the findings. This paper initials a spectrum of uncertain random singular game, and investigates two‐person nonzero‐sum as well as zero‐sum games for uncertain random singular dynamic systems.