On Solutions of the Riccati Equation in Optimization Problems

Bernard Friedland

doi:10.1109/TAC.1967.1098602

On Solutions of the Riccati Equation in Optimization Problems

Bernard Friedland

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The difference D between two solutions S and M of the matrix Riccati equation [formula omitted] is given by D=RQ-1R’, where [formula omitted] and [formula omitted]. These relations can be used to evaluate M(t) for t < T arising in optimization problems in which M(T) does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.

Original language	English (US)
Pages (from-to)	303-304
Number of pages	2
Journal	IEEE Transactions on Automatic Control
Volume	AC-12
Issue number	3
DOIs	https://doi.org/10.1109/TAC.1967.1098602
State	Published - Jun 1967
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.1967.1098602

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title = "On Solutions of the Riccati Equation in Optimization Problems",

abstract = "The difference D between two solutions S and M of the matrix Riccati equation [formula omitted] is given by D=RQ-1R{\textquoteright}, where [formula omitted] and [formula omitted]. These relations can be used to evaluate M(t) for t < T arising in optimization problems in which M(T) does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.",

author = "Bernard Friedland",

year = "1967",

month = jun,

doi = "10.1109/TAC.1967.1098602",

language = "English (US)",

volume = "AC-12",

pages = "303--304",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

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T1 - On Solutions of the Riccati Equation in Optimization Problems

AU - Friedland, Bernard

PY - 1967/6

Y1 - 1967/6

N2 - The difference D between two solutions S and M of the matrix Riccati equation [formula omitted] is given by D=RQ-1R’, where [formula omitted] and [formula omitted]. These relations can be used to evaluate M(t) for t < T arising in optimization problems in which M(T) does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.

AB - The difference D between two solutions S and M of the matrix Riccati equation [formula omitted] is given by D=RQ-1R’, where [formula omitted] and [formula omitted]. These relations can be used to evaluate M(t) for t < T arising in optimization problems in which M(T) does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.

UR - https://www.scopus.com/pages/publications/0011009038

UR - https://www.scopus.com/pages/publications/0011009038#tab=citedBy

U2 - 10.1109/TAC.1967.1098602

DO - 10.1109/TAC.1967.1098602

M3 - Article

AN - SCOPUS:0011009038

SN - 0018-9286

VL - AC-12

SP - 303

EP - 304

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -

On Solutions of the Riccati Equation in Optimization Problems

Abstract

All Science Journal Classification (ASJC) codes

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