On the computation of switching surfaces in optimal control: A Gröbner basis approach

Uli Walther; Tryphon T. Georgiou; Allen Tannenbaum

doi:10.1109/9.917655

On the computation of switching surfaces in optimal control: A Gröbner basis approach

Uli Walther, Tryphon T. Georgiou, Allen Tannenbaum

Electrical and Computer Engineering

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

14 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 Gröbner bases. In this paper, we apply the Gröbner basis technique to find effective solutions to the classical problem of time-optimal control.

Original language	English (US)
Pages (from-to)	534-540
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	46
Issue number	4
DOIs	https://doi.org/10.1109/9.917655
State	Published - Apr 2001

Bibliographical note

Funding Information:
Manuscript received March 17, 1999; revised June 6, 2000. Recommended by Associate Editor P. Voulgaris. The work of U. Walther was supported by the A.P. Sloan Foundation. The work of T. T. Georgiou and A. Tan-nenbaum was supported by Grants from the National Science Foundation ECS-99700588, ECS-9505995, NSF-LIS, Air Force Office of Scientific Research AF/F49620-98-1-0168, AF/F49620-96-1-0094 by the Army Research Office DAAG55-98-1-0169, and MURI Grant.

Keywords

Computation algebraic geometry
Gröbner bases
Optimal control
Switching surfaces

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On the computation of switching surfaces in optimal control: A Gröbner basis approach

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Keywords

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