Robust output Nash strategies based on sliding mode observation in a two-player differential game

This paper tackles the problem of a two-player differential game affected by matched uncertainties with only the output measurement available for each player. We suggest a state estimation based on the so-called algebraic hierarchical observer for each player in order to design the Nash equilibrium strategies based on such estimation. At the same time, the use of an output integral sliding mode term (also based on the estimation processes) for the Nash strategies robustification for both players ensures the compensation of the matched uncertainties. A simulation example shows the feasibility of this approach in a magnetic levitator problem.