Robust Nash Strategies based on Integral Sliding Mode Control for a Two Players Uncertain LQ Game

This paper tackles the problem of a two players linear quadratic multi-model linear quadratic (LQ) differential game affected with matched uncertainties. Based on a recent result of a robust Nash equilibrium for a multi- modeled LQ game, where the players compose a min-max strategy to deal with the parametric uncertainties (unmatched type) in this paper we add second type or uncertainties of the "matched type". It is shown that for the case of two players game, the matched uncertainties can be rejected from the initial time introducing in the strategies an integral sliding mode control term, obtaining a equivalent game dynamic in which the matched uncertainties have been eliminated.