Equilibrium in Nash differential games via Lyapunov-type iterations

This paper discusses the numerical solution of the coupled algebraic Riccati equations associated with the linear quadratic differential games. The Lyapunov iteration for solving the considered coupled equations is discussed by Li and Gajic (1994). We modify this iteration and derive the new algorithm with typically convergence properties for methods of such a type introduced in the literature. Finally, to demonstrate the efficiency of the proposed algorithms, computational examples are provided and numerical effectiveness of the considered algorithms is commented.