Partitioned Riccati algorithms

Abstract

Generalized partitioned solutions of Riccati equations are presented in terms of forward and backward-time differentiations that are theoretically interesting, computationally attractive, as well as they provide important new interpretations of these results. This approach leads also to important generalizations of previous Riccati solutions such as the Chandrasekhar and the partitioned algorithms. Specifically, it is shown that the generalized partitioned solutions may be given in terms of a generalized Chandrasekhar algorithm. These generalizations pertain to arbitrary initial conditions and time-varying models. Furthermore, based on these partitioned solutions, robust and fast algorithms are obtained for the effective numerical solution of Riccati equations. A particularly effective doubling algorithm is also given for calculating the steady-state solution of time-invariant Riccati equations. The partitioned algorithms are given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation on the elemental solutions.