Temporal difference methods for the maximal solution of discrete-time coupled algebraic Riccati equations

In this paper, we present an iterative technique for deriving the maximal s olution of a set of discrete-time coupled algebraic Riccati equations, base d on temporal difference methods, which are related to the optimal control of Markovian jump linear systems and have been studied extensively over the last few years. We trace a parallel with the theory of temporal difference algorithms for Markovian decision processes to develop a lambda -policy it eration like algorithm for the maximal solution of these equations. For the special cases in which lambda =0 and lambda = 1 we have the situation in w hich the algorithm reduces to the iterations of the Riccati difference equa tions (value iteration) and quasilinearization method (policy iteration), r espectively. The advantage of the proposed method is that an appropriate ch oice of lambda between 0 and 1 can speed up the convergence of the policy e valuation step of the policy iteration method by using value iteration.