Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

Lin Du, Weiming Xiang, Yongchi Zhao

Research output: Contribution to journalArticle

Abstract

The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.

Original languageEnglish (US)
Article number512485
JournalMathematical Problems in Engineering
Volume2014
DOIs
StatePublished - Jan 1 2014

Fingerprint

Switched Systems
Switching frequency
State Estimation
State estimation
Discrete-time Systems
Observer
Finite-time Stability
Switched Linear Systems
Asymptotic stability
Short Intervals
Linear systems
Genetic algorithms
Asymptotic Stability
Chemical activation
Switches
Iterative Algorithm
Activation
Switch
Disturbance
Genetic Algorithm

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint. / Du, Lin; Xiang, Weiming; Zhao, Yongchi.

In: Mathematical Problems in Engineering, Vol. 2014, 512485, 01.01.2014.

Research output: Contribution to journalArticle

@article{67b5f1dd152c4729b4a838114fb4ee70,
title = "Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint",
abstract = "The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.",
author = "Lin Du and Weiming Xiang and Yongchi Zhao",
year = "2014",
month = "1",
day = "1",
doi = "10.1155/2014/512485",
language = "English (US)",
volume = "2014",
journal = "Mathematical Problems in Engineering",
issn = "1024-123X",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

AU - Du, Lin

AU - Xiang, Weiming

AU - Zhao, Yongchi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.

AB - The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed. Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems. By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest. Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances. Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm. A numerical example is provided to illustrate the theoretical findings in this paper.

UR - http://www.scopus.com/inward/record.url?scp=84934898628&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84934898628&partnerID=8YFLogxK

U2 - 10.1155/2014/512485

DO - 10.1155/2014/512485

M3 - Article

AN - SCOPUS:84934898628

VL - 2014

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 512485

ER -