Zames-Falb multipliers for quadratic programming

William P. Heath; Adrian G. Wills

doi:10.1109/TAC.2007.906233

Zames-Falb multipliers for quadratic programming

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

Abstract

In constrained linear model predictive control, a quadratic program must be solved on-line at each control step, and this constitutes a nonlinearity. If zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded. We show that if the nonlinearity is static then it is also monotone and slope restricted; hence, we show the existence of Zames-Falb multipliers for such a nonlinearity. The multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control. © 2007 IEEE.

Original language	English
Pages (from-to)	1948-1951
Number of pages	3
Journal	IEEE Transactions on Automatic Control
Volume	52
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2007.906233
Publication status	Published - Oct 2007

Keywords

Integral quadratic constraint (IQC)
Nonlinear stability

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10.1109/TAC.2007.906233

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title = "Zames-Falb multipliers for quadratic programming",

abstract = "In constrained linear model predictive control, a quadratic program must be solved on-line at each control step, and this constitutes a nonlinearity. If zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded. We show that if the nonlinearity is static then it is also monotone and slope restricted; hence, we show the existence of Zames-Falb multipliers for such a nonlinearity. The multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control. {\textcopyright} 2007 IEEE.",

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AB - In constrained linear model predictive control, a quadratic program must be solved on-line at each control step, and this constitutes a nonlinearity. If zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded. We show that if the nonlinearity is static then it is also monotone and slope restricted; hence, we show the existence of Zames-Falb multipliers for such a nonlinearity. The multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control. © 2007 IEEE.

KW - Integral quadratic constraint (IQC)

KW - Nonlinear stability

U2 - 10.1109/TAC.2007.906233

DO - 10.1109/TAC.2007.906233

M3 - Article

SN - 1558-2523

SN - 2334-3303

VL - 52

SP - 1948

EP - 1951

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

ER -

Zames-Falb multipliers for quadratic programming

Abstract

Keywords

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