A bilevel programming approach to the convergence analysis of control-lyapunov functions

Wentao Tang; Prodromos Daoutidis

doi:10.1109/TAC.2019.2892386

A bilevel programming approach to the convergence analysis of control-lyapunov functions

Wentao Tang, Prodromos Daoutidis

Chemical Engineering and Materials Science

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

8 Scopus citations

Abstract

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min-max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush- Kuhn-Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.

Original language	English (US)
Article number	8610152
Pages (from-to)	4174-4179
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	64
Issue number	10
DOIs	https://doi.org/10.1109/TAC.2019.2892386
State	Published - Oct 2019

Bibliographical note

Funding Information:
Manuscript received April 3, 2018; revised August 20, 2018 and December 19, 2018; accepted December 30, 2018. Date of publication January 11, 2019; date of current version September 25, 2019. This work was supported by the National Science Foundation (NSF-CBET). Recommended by Associate Editor F. Mazenc. (Corresponding author: Prodromos Daoutidis.) The authors are with the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,tangx647@umn.edu; daout001@umn.edu).

Publisher Copyright:
© 2019 IEEE.

Keywords

Bilevel programming
Control-Lyapunov function
Domain of attraction
Lyapunov stability

Access

10.1109/TAC.2019.2892386

OpenUrl availability

Full text

Cite this

@article{1973e7bd271e4fd1b9c51ba7d894d383,

title = "A bilevel programming approach to the convergence analysis of control-lyapunov functions",

abstract = "This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min-max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush- Kuhn-Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.",

keywords = "Bilevel programming, Control-Lyapunov function, Domain of attraction, Lyapunov stability",

author = "Wentao Tang and Prodromos Daoutidis",

note = "Funding Information: Manuscript received April 3, 2018; revised August 20, 2018 and December 19, 2018; accepted December 30, 2018. Date of publication January 11, 2019; date of current version September 25, 2019. This work was supported by the National Science Foundation (NSF-CBET). Recommended by Associate Editor F. Mazenc. (Corresponding author: Prodromos Daoutidis.) The authors are with the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,tangx647@umn.edu; daout001@umn.edu). Publisher Copyright: {\textcopyright} 2019 IEEE.",

year = "2019",

month = oct,

doi = "10.1109/TAC.2019.2892386",

language = "English (US)",

volume = "64",

pages = "4174--4179",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

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

number = "10",

}

TY - JOUR

T1 - A bilevel programming approach to the convergence analysis of control-lyapunov functions

AU - Tang, Wentao

AU - Daoutidis, Prodromos

N1 - Funding Information: Manuscript received April 3, 2018; revised August 20, 2018 and December 19, 2018; accepted December 30, 2018. Date of publication January 11, 2019; date of current version September 25, 2019. This work was supported by the National Science Foundation (NSF-CBET). Recommended by Associate Editor F. Mazenc. (Corresponding author: Prodromos Daoutidis.) The authors are with the Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,tangx647@umn.edu; daout001@umn.edu). Publisher Copyright: © 2019 IEEE.

PY - 2019/10

Y1 - 2019/10

N2 - This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min-max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush- Kuhn-Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.

AB - This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min-max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush- Kuhn-Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption.

KW - Bilevel programming

KW - Control-Lyapunov function

KW - Domain of attraction

KW - Lyapunov stability

UR - http://www.scopus.com/inward/record.url?scp=85075566149&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075566149&partnerID=8YFLogxK

U2 - 10.1109/TAC.2019.2892386

DO - 10.1109/TAC.2019.2892386

M3 - Article

AN - SCOPUS:85075566149

SN - 0018-9286

VL - 64

SP - 4174

EP - 4179

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 10

M1 - 8610152

ER -

A bilevel programming approach to the convergence analysis of control-lyapunov functions

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this