Nonlinear state feedback for ℓ1 optimal control

Jeff S. Shamma

doi:10.1016/0167-6911(93)90067-G

Nonlinear state feedback for ℓ¹ optimal control

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

Abstract

This paper considers ℓ¹ optimal control problems with full state feedback. In contrast to H^∞ optimal control, previous work has shown that linear ℓ¹ optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.

Original language	English (US)
Pages (from-to)	265-270
Number of pages	6
Journal	Systems and Control Letters
Volume	21
Issue number	4
DOIs	https://doi.org/10.1016/0167-6911(93)90067-G
State	Published - Oct 1993
Externally published	Yes

Keywords

Disturbance rejection
nonlinear compensation
state feedback
viability theory
ℓ optimal control

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Online availability

10.1016/0167-6911(93)90067-G

Library availability

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Cite this

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title = "Nonlinear state feedback for ℓ1 optimal control",

abstract = "This paper considers ℓ1 optimal control problems with full state feedback. In contrast to H∞ optimal control, previous work has shown that linear ℓ1 optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.",

keywords = "Disturbance rejection, nonlinear compensation, state feedback, viability theory, ℓ optimal control",

author = "Shamma, {Jeff S.}",

note = "Funding Information: Correspondence to: J.S. Shamma, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712, USA * Supported by AFOSR Research Initiation grant #92-70 sub-contracted to the Research and Development Laboratory and NSF grants # ECS-9296074 and # ECS-9258005.",

year = "1993",

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journal = "Systems and Control Letters",

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N1 - Funding Information: Correspondence to: J.S. Shamma, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712, USA * Supported by AFOSR Research Initiation grant #92-70 sub-contracted to the Research and Development Laboratory and NSF grants # ECS-9296074 and # ECS-9258005.

PY - 1993/10

Y1 - 1993/10

N2 - This paper considers ℓ1 optimal control problems with full state feedback. In contrast to H∞ optimal control, previous work has shown that linear ℓ1 optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.

AB - This paper considers ℓ1 optimal control problems with full state feedback. In contrast to H∞ optimal control, previous work has shown that linear ℓ1 optimal controllers can be dynamic and arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback perform as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.

KW - Disturbance rejection

KW - nonlinear compensation

KW - state feedback

KW - viability theory

KW - ℓ optimal control

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