Recursive solution of linear-quadratic Nash games for weakly interconnected systems (Q1091319)

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence of \(0(\epsilon ^ 2)\), where \(\epsilon\) is a small coupling parameter. In addition, only low- order systems are involved in algebraic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.