Fast Riccati equation solutions: Partitioned algorithms

In this paper, using the ‘partitioning’ approach to estimation, exceptionally robust and fast computational algorithms for the effective solution of continuous Riccati equations are presented. The algorithms have essentially a decomposed or ‘partitioned’ structure which is both theoretically interesting as well as computationally attractive. Specifically, the ‘partitioned’ solution is given exactly in terms of a set of elemental solutions which are both simple as well as completely decoupled from each other, and as such computable in either a parallel or serial processing mode. Moreover, the overall solution is given by a simple recursive operation of the elemental solution. Extensive computer simulation has shown that the ‘partitioned’ algorithm is numerically very effective and robust, especially in the case of ill-conditioned Riccati solutions, e.g. for ill-conditioned initial conditions, or for stiff system matrices. Further, the ‘partitioned’ algorithm is very fast, ranging up to several orders of magnitude faster than the corresponding Runge-Kutta algorithm.