Newton-like method for solving generalized algebraic Riccati equation of feedback linear quadratic game

In this paper, we consider a Nash equilibrium problem of linear quadratic dynamic games with two players. We assume that the players give a linear feedback to the game. As a typical control problem, for the game with infinite planning horizon, finding optimal control become a problem of finding solution of algebraic Riccati equation. In this paper, we will solve the generalized algebraic Riccati equation that arising from the linear quadratic dynamic game with feedback numerically. We use a Newton-like method for solving the generalized algebraic Riccati equation which is called exact line search method. This method will improve the convergence behaviour of Newton's method. It will accelerates convergence when Newton iterations are too long.