The Recursive Solution of Linear Quadratic Nash Games for Weakly Interconnected Systems

The recursive method was developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that each iteration step improves the accuracy by an order of magnitude, i.e., the accuracy of O(¿^k), (where ¿ is a coupling parameter) can be obtained by doing only k-l iterations. On the other hand, only low-order systems are involved in algebraic computations, and no analicity requirements are imposed on the system coefficients.