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- Title
Saddle-point solution to zero-sumgame for uncertain noncausal systems based on optimistic value.
- Authors
Chen, Xin; Wang, Yan; Li, Fuzhen; Shao, Yu
- Abstract
Uncertain noncausal systems (UNCSs) are uncertain singular systems that are supposed to be regular along.This study investigates two-player zero-sum games (TPZSGs) for UNCSs using the optimistic value criterion. The first step is to introduce a method to convert a linear uncertain noncausal system (UNCS) considering linear control terms into subsystems including two kinds of uncertain difference equations. Recurrence equations are derived for tackling a TPZSG subject to linear UNCSs. Using recurrence equations, we give an algorithm for solving the TPZSG subject to linear UNCSs and show how to apply the algorithm to find the saddle-point solution and the equilibrium value of this kind of game by a numerical example. To expand on these results, we provide the corresponding equations for solving TPZSGs subject to nonlinear UNCSs. Moreover, we give the saddle-point solution and equilibrium value of a TPZSG for a nonlinear UNCS considering quadratic control terms by solving the equations.
- Subjects
UNCERTAIN systems; ZERO sum games; DIFFERENCE equations; EQUATIONS; FEMTOCELLS
- Publication
Journal of Industrial & Management Optimization, 2024, Vol 20, Issue 4, p1
- ISSN
1547-5816
- Publication type
Article
- DOI
10.3934/jimo.2023135