ℓ1 State-feedback control with a prescribed rate of exponential convergence

Ian J. Fialho; Tryphon T. Georgiou

doi:10.1109/9.633846

ℓ₁ State-feedback control with a prescribed rate of exponential convergence

Ian J. Fialho, Tryphon T. Georgiou

Electrical and Computer Engineering

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

9 Scopus citations

Abstract

In this paper we consider the ℓ₁ -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ₁ performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ₁-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ₁ performance.

Original language	English (US)
Pages (from-to)	1476-1481
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	42
Issue number	10
DOIs	https://doi.org/10.1109/9.633846
State	Published - 1997

Bibliographical note

Funding Information:
Manuscript received July 19, 1995; revised June 15, 1996 and October 21, 1996. This work was supported in part by the NSF under Grant NSF/ECS-9016050 and the AFOSR under Grant AF/F49620-92-J-0241. I. J. Fialho is with the Department of Aerospace Engineering, University of Minnesota, Minneapolis, MN 55455 USA. T. T. Georgiou is with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455 USA. Publisher Item Identifier S 0018-9286(97)05957-6.

Keywords

Controlled-invariant sets
Isaacs equation
ℓ control

Publisher link

10.1109/9.633846

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title = "ℓ1 State-feedback control with a prescribed rate of exponential convergence",

abstract = "In this paper we consider the ℓ1 -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ1 performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ1-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ1 performance.",

keywords = "Controlled-invariant sets, Isaacs equation, ℓ control",

author = "Fialho, {Ian J.} and Georgiou, {Tryphon T.}",

note = "Funding Information: Manuscript received July 19, 1995; revised June 15, 1996 and October 21, 1996. This work was supported in part by the NSF under Grant NSF/ECS-9016050 and the AFOSR under Grant AF/F49620-92-J-0241. I. J. Fialho is with the Department of Aerospace Engineering, University of Minnesota, Minneapolis, MN 55455 USA. T. T. Georgiou is with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455 USA. Publisher Item Identifier S 0018-9286(97)05957-6.",

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AU - Georgiou, Tryphon T.

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N2 - In this paper we consider the ℓ1 -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ1 performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ1-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ1 performance.

AB - In this paper we consider the ℓ1 -state feedback problem with an internal stability constraint. In particular, we establish the connection between controlled-invariant contractive sets and static control laws that achieve a level of ℓ1 performance as well as a desired unforced rate of convergence. We outline two algorithms for computing controlled-invariant contractive sets. The first is a modification of standard recursive techniques used in the literature, where as the second is based on dynamic games and involves solving an appropriate discrete Isaacs recursion. The latter approach results in a min-max characterization of ℓ1-state feedback controllers. We point out that the Isaacs recursion provides a one-shot (as opposed to iterative) computation of the optimal ℓ1 performance.

KW - Controlled-invariant sets

KW - Isaacs equation

KW - ℓ control

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