Superposition laws for solutions of differential matrix Riccati equations arising in control theory

Author

Sorine, Michel ; Winternitz, Pavel

Author_Institution

Institut National de Recherche en Informatique et an Automatique, Le Chesnay, France

Volume

30

Issue

3

fYear

1985

fDate

3/1/1985 12:00:00 AM

Firstpage

266

Lastpage

272

Abstract

Representation formulas are given for the general solution of the $N \\times N$ matrix Riccati equation $\\dot{W} = A + WB + CW + WDW$ using $n$ known solutions, with $n = 1, ..., 5$ ( $n$ -representations). The 5- representation is a superposition formula, in that it expresses the general solution explicitly as a function of five particular solutions and N²arbitrary constants ( $N \\geq 2$ ), using no further information. The representation formulas can be used in numerical calculations. The 4- and 5- representations are specially useful when a solution $W(t)$ has a singularity for some finite $t = t_{0}$ . They also clarify the properties of the solution space: the matrix elements of $W(t)$ are meromorphic functions of $t$ having simple poles as the only possible singularities. The relation between the representation formulas and previously known results is discussed.

Keywords

Differential Riccati equations; Riccati equations, differential; Algebra; Control theory; Councils; Differential equations; Filtering; Helium; Nonlinear equations; Optimal control; Riccati equations; Terminology;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1985.1103934

Filename

1103934