Carleman approximation based quasi-analytic model predictive control for nonlinear systems

Yizhou Fang, Antonios Armaou

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

This manuscript aims at developing a nonlinear model predictive controller formulation based on Carleman approximation. It approximates the nonlinear dynamic constraints with polynomial ones through Taylor expansion. Then, it extends the state variables to higher orders following the Kronecker product rule and expresses the nonlinear dynamic constraints with an extended bilinear representation. With little loss of nonlinear information, the formulation enables analytical prediction of future states. It also analytically calculates the sensitivity of the cost function to the manipulated inputs to facilitate the search algorithm by serving as the gradient. We present a brief analysis of error accumulation caused by Carleman approximation and then improve the accuracy of the approach by resetting extended states periodically. The idea of efficient temporal discretization is embedded in control vector parameterization to improve the controller performance. The advantages are illustrated in two applications where we solve a tracking problem and a regulation problem.

Original languageEnglish (US)
Pages (from-to)3915-3929
Number of pages15
JournalAIChE Journal
Volume62
Issue number11
DOIs
StatePublished - Nov 1 2016

Fingerprint

Nonlinear Dynamics
Model predictive control
Nonlinear systems
Controllers
Parameterization
Cost functions
Polynomials
Costs and Cost Analysis

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

Cite this

@article{71bbae5e9a634dc08d24d3794cea5f9c,
title = "Carleman approximation based quasi-analytic model predictive control for nonlinear systems",
abstract = "This manuscript aims at developing a nonlinear model predictive controller formulation based on Carleman approximation. It approximates the nonlinear dynamic constraints with polynomial ones through Taylor expansion. Then, it extends the state variables to higher orders following the Kronecker product rule and expresses the nonlinear dynamic constraints with an extended bilinear representation. With little loss of nonlinear information, the formulation enables analytical prediction of future states. It also analytically calculates the sensitivity of the cost function to the manipulated inputs to facilitate the search algorithm by serving as the gradient. We present a brief analysis of error accumulation caused by Carleman approximation and then improve the accuracy of the approach by resetting extended states periodically. The idea of efficient temporal discretization is embedded in control vector parameterization to improve the controller performance. The advantages are illustrated in two applications where we solve a tracking problem and a regulation problem.",
author = "Yizhou Fang and Antonios Armaou",
year = "2016",
month = "11",
day = "1",
doi = "10.1002/aic.15298",
language = "English (US)",
volume = "62",
pages = "3915--3929",
journal = "AICHE Journal",
issn = "0001-1541",
publisher = "American Institute of Chemical Engineers",
number = "11",

}

Carleman approximation based quasi-analytic model predictive control for nonlinear systems. / Fang, Yizhou; Armaou, Antonios.

In: AIChE Journal, Vol. 62, No. 11, 01.11.2016, p. 3915-3929.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Carleman approximation based quasi-analytic model predictive control for nonlinear systems

AU - Fang, Yizhou

AU - Armaou, Antonios

PY - 2016/11/1

Y1 - 2016/11/1

N2 - This manuscript aims at developing a nonlinear model predictive controller formulation based on Carleman approximation. It approximates the nonlinear dynamic constraints with polynomial ones through Taylor expansion. Then, it extends the state variables to higher orders following the Kronecker product rule and expresses the nonlinear dynamic constraints with an extended bilinear representation. With little loss of nonlinear information, the formulation enables analytical prediction of future states. It also analytically calculates the sensitivity of the cost function to the manipulated inputs to facilitate the search algorithm by serving as the gradient. We present a brief analysis of error accumulation caused by Carleman approximation and then improve the accuracy of the approach by resetting extended states periodically. The idea of efficient temporal discretization is embedded in control vector parameterization to improve the controller performance. The advantages are illustrated in two applications where we solve a tracking problem and a regulation problem.

AB - This manuscript aims at developing a nonlinear model predictive controller formulation based on Carleman approximation. It approximates the nonlinear dynamic constraints with polynomial ones through Taylor expansion. Then, it extends the state variables to higher orders following the Kronecker product rule and expresses the nonlinear dynamic constraints with an extended bilinear representation. With little loss of nonlinear information, the formulation enables analytical prediction of future states. It also analytically calculates the sensitivity of the cost function to the manipulated inputs to facilitate the search algorithm by serving as the gradient. We present a brief analysis of error accumulation caused by Carleman approximation and then improve the accuracy of the approach by resetting extended states periodically. The idea of efficient temporal discretization is embedded in control vector parameterization to improve the controller performance. The advantages are illustrated in two applications where we solve a tracking problem and a regulation problem.

UR - http://www.scopus.com/inward/record.url?scp=84971317629&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84971317629&partnerID=8YFLogxK

U2 - 10.1002/aic.15298

DO - 10.1002/aic.15298

M3 - Article

AN - SCOPUS:84971317629

VL - 62

SP - 3915

EP - 3929

JO - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 11

ER -