Saddle-point solution to zero-sumgame for uncertain noncausal systems based on optimistic value

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.