Equilibrium in LQ differential games with multiple scenarios

This paper tackles the problem of finding a Nash-equilibrium for a differential game with multiple scenarios or multiple models of the game. Player´s dynamics is governed by an ordinary differential equation with unknown parameters (Multi-Model representation) from a given finite set. The problem consists in the designing of min-max strategies for each player which guarantee an equilibrium for the worst case scenario. Based on the Robust Maximum Principle necessary conditions for a game to be in Robust Nash Equilibrium are derived. The LQ differential games are considered in detail. It is shown that the initial min-max differential game may be converted in to a standard static game given in a multidimensional simplex. A numerical procedure for resolving the LQ differential game is designed.