Robust Nash Equilibrium in multi-model LQ differential games: analysis and extraproximal numerical procedure

This paper tackles the problem of finding a Nash equilibrium for a multi-model differential 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 into a standard static game given in a multi-dimensional simplex. A numerical procedure for resolving the LQ differential game is designed.