A group-theoretical approach to optimal estimation and control
type: Item
instance of: scholarly article
title: A group-theoretical approach to optimal estimation and control
zbMATH Open document ID: 0549.93068
DOI: 10.1016/0022-247X(83)90205-6
author: S. J. Orfanidis
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 93E25
zbMATH DE Number: 3877053
zbMATH Keywords: symplectic group structure
zbMATH Keywords: matrix Riccati equation
zbMATH Keywords: partitioning algorithms
zbMATH Keywords: integration-free Chandrasekhar type algorithm
reviewed by: Spyros G. Tzafestas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3877053