Finite Time Robust Feedback Nash Equilibrium for Linear Quadratic Games

Abstract

In this paper we consider the solution for an N players non-cooperative differential game affected by some sort of uncertainties. The problem analyzed is linear quadratic in nature, and the uncertainty affecting the game is square integrable, which is seen as a malicious fictitious player trying to maximize the cost function of each player. In order to find the solution to this problem we solve a robust form of the Hamilton-Jacobi-Bellman equation, which allows us to find the robust equilibrium strategies for each player and in turn to solve a Coupled Riccati Differential Equation.