Computational algebraic geometry and switching surfaces in optimal control

Uli Walther; Tryphon Georgiou; Allen Tannenbaum

Computational algebraic geometry and switching surfaces in optimal control

Uli Walther, Tryphon Georgiou, Allen Tannenbaum

Electrical and Computer Engineering

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this note, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.

Original language	English (US)
Pages (from-to)	4724-4729
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	5
State	Published - 1999
Event	The 38th IEEE Conference on Decision and Control (CDC) - Phoenix, AZ, USA Duration: Dec 7 1999 → Dec 10 1999

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title = "Computational algebraic geometry and switching surfaces in optimal control",

abstract = "A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this note, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.",

author = "Uli Walther and Tryphon Georgiou and Allen Tannenbaum",

year = "1999",

language = "English (US)",

volume = "5",

pages = "4724--4729",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0191-2216",

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

note = "The 38th IEEE Conference on Decision and Control (CDC) ; Conference date: 07-12-1999 Through 10-12-1999",

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T1 - Computational algebraic geometry and switching surfaces in optimal control

AU - Walther, Uli

AU - Georgiou, Tryphon

AU - Tannenbaum, Allen

PY - 1999

Y1 - 1999

N2 - A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this note, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.

AB - A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this note, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.

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M3 - Conference article

AN - SCOPUS:0033311582

SN - 0191-2216

VL - 5

SP - 4724

EP - 4729

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - The 38th IEEE Conference on Decision and Control (CDC)

Y2 - 7 December 1999 through 10 December 1999

ER -

Computational algebraic geometry and switching surfaces in optimal control

Abstract

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