A group-theoretical approach to optimal estimation and control
This paper exploits the symplectic group structure associated with the matrix Riccati equation for deriving a unifying group-theoretical framework involving several well known results. Among them are all efficient algorithmic ways of integrating the Riccati system, such as integration-free iterative algorithms, doubling and Chandrasekhar-type algorithms which are shown to be simple consequences of the group nature of the problem. Partitioning algorithms relating different Riccati solutions are also included in this framework with group-theoretical significance corresponding to invariance under group multiplication from the right. The group structure is further used for deriving a new integration-free Chandrasekhar type algorithm, and to present a fairly complete characterization of solutions of the Riccati equation in the periodic case. The results of the paper actually enlarge the applications repertory of using the equivalence between the Riccati equation and the associated linearized Hamiltonian formulation.
integration-free Chandrasekhar type algorithm
scientific article; zbMATH DE number 3877053
scientific article