Uniqueness of optimal controls in L∞

S. D. Fisher; J. W. Jerome

doi:10.1007/BF00933091

Uniqueness of optimal controls in L^∞

S. D. Fisher^*, J. W. Jerome

^*Corresponding author for this work

Mathematics

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

Abstract

We consider those functions u∈L^∞(a, b) which satisfy X′=Ax+Bu, where X satisfies certain prescribed interpolatory constraints. We show that there is a u with smallest sup norm and that such u are uniquely determined on a certain subset of [a, b]; more restrictions allow us to conclude that X is uniquely determined on this set. An extension is given to certain linear control systems on the real line.

Original language	English (US)
Pages (from-to)	469-476
Number of pages	8
Journal	Journal of Optimization Theory and Applications
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/BF00933091
State	Published - Apr 1 1977

Keywords

Linear control system
bang-bang principle
interval of uniqueness

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Access to Document

10.1007/BF00933091

Cite this

@article{d2be8579147140b28e9f32df595c4a03,

title = "Uniqueness of optimal controls in L∞",

abstract = "We consider those functions u∈L∞(a, b) which satisfy X′=Ax+Bu, where X satisfies certain prescribed interpolatory constraints. We show that there is a u with smallest sup norm and that such u are uniquely determined on a certain subset of [a, b]; more restrictions allow us to conclude that X is uniquely determined on this set. An extension is given to certain linear control systems on the real line.",

keywords = "Linear control system, bang-bang principle, interval of uniqueness",

author = "Fisher, {S. D.} and Jerome, {J. W.}",

year = "1977",

month = apr,

day = "1",

doi = "10.1007/BF00933091",

language = "English (US)",

volume = "21",

pages = "469--476",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Uniqueness of optimal controls in L∞

AU - Fisher, S. D.

AU - Jerome, J. W.

PY - 1977/4/1

Y1 - 1977/4/1

N2 - We consider those functions u∈L∞(a, b) which satisfy X′=Ax+Bu, where X satisfies certain prescribed interpolatory constraints. We show that there is a u with smallest sup norm and that such u are uniquely determined on a certain subset of [a, b]; more restrictions allow us to conclude that X is uniquely determined on this set. An extension is given to certain linear control systems on the real line.

AB - We consider those functions u∈L∞(a, b) which satisfy X′=Ax+Bu, where X satisfies certain prescribed interpolatory constraints. We show that there is a u with smallest sup norm and that such u are uniquely determined on a certain subset of [a, b]; more restrictions allow us to conclude that X is uniquely determined on this set. An extension is given to certain linear control systems on the real line.

KW - Linear control system

KW - bang-bang principle

KW - interval of uniqueness

UR - http://www.scopus.com/inward/record.url?scp=34250297299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250297299&partnerID=8YFLogxK

U2 - 10.1007/BF00933091

DO - 10.1007/BF00933091

M3 - Article

AN - SCOPUS:34250297299

SN - 0022-3239

VL - 21

SP - 469

EP - 476

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 4

ER -