Advanced search
Publication Cover
International Journal of Control Volume 93, 2020 - Issue 11: Interval estimation applied to diagnosis and control
Submit an article Journal homepage
194
Views
3
CrossRef citations to date
0
Altmetric
Articles

Interval state estimation for uncertain polytopic systems

Benoît Marxa Université de Lorraine, CNRS, CRAN, Nancy, France
,
Dalil Ichalalb IBISC, University of Evry, Paris-Saclay University, Evry Courcouronnes, France
&
José Ragota Université de Lorraine, CNRS, CRAN, Nancy, FranceCorrespondence[email protected]
Pages 2564-2576 | Received 21 May 2018, Accepted 09 Jul 2019, Published online: 21 Jul 2019
 
Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days

Abstract

The aim of this article is the state estimation of uncertain polytopic dynamic systems. The parametric uncertainties affecting the system are time varying, unknown and bounded with known bounds. The objective is to determine the state estimates consisting in the smallest interval containing the real-state value caused by the parametric uncertainties. This set will be characterised by the lower and upper bounds of the state trajectory. Given the uncertainty bounds, the set can be computed by a direct simulation of the system but a more accurate estimation is obtained with a Luenberger-type observer, fed with the system measurements. The proposed observer is designed to minimise the interval width of the estimates. The observer gains are obtained by solving an optimisation problem under LMI constraints. The efficiency of the proposed approach is illustrated by numerical examples.

Disclosure statement

No potential conflict of interest was reported by the authors.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

Linear Matrix Inequalities in System and Control Theory
Source: Society for Industrial and Applied Mathematics
Interval observer framework for fault-tolerant control of linear parameter-varying systems
Source: Informa UK Limited
Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach
Source: Institute of Electrical and Electronics Engineers (IEEE)
The normalized interval regression model with outlier detection and its real-world application to house pricing problems
Source: Elsevier BV
An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model
Source: Walter de Gruyter GmbH
State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers
Source: Informa UK Limited
Control of non-linear switched systems with average dwell time: interval observer-based framework
Source: Institution of Engineering and Technology (IET)
Recursive state bounding by parallelotopes
Source: Elsevier BV
Linear Matrix Inequalities in System and Control Theory
Source: Society for Industrial and Applied Mathematics
Interval Observer-Based Fault Isolation for Discrete-Time Fuzzy Interconnected Systems With Unknown Interconnections
Source: Institute of Electrical and Electronics Engineers (IEEE)
Design of interval observers for uncertain dynamical systems
Source: Pleiades Publishing Ltd
An introduction to observers
Source: Institute of Electrical and Electronics Engineers (IEEE)
Diagonal stability of interval matrices and applications
Source: Elsevier BV
Interval observer design for uncertain discrete-time linear systems
Source: Elsevier BV
Interval observer design for LPV systems with parametric uncertainty
Source: Elsevier BV
Interval observer for LPV systems with unknown inputs
Source: HAL CCSD
Fault detection and isolation using viability theory and interval observers
Source: Informa UK Limited
Sensitivity and inverse analysis methods for parameter intervals
Source: Elsevier BV
Nonlinear Observers and Applications
Source: Springer Berlin Heidelberg
Exponential stabilization of stochastic interval system with time dependent parameters
Source: Elsevier BV
State estimation of Takagi–Sugeno systems with unmeasurable premise variables
Source: Institution of Engineering and Technology (IET)
A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks
Source: Elsevier BV
Interval Observers for Time-Varying Discrete-Time Systems
Source: Institute of Electrical and Electronics Engineers (IEEE)
Parameterized linear matrix inequality techniques in fuzzy control system design
Source: Institute of Electrical and Electronics Engineers (IEEE)
Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data
Source: Elsevier BV
Fuzzy Control Systems Design and Analysis
Source: John Wiley & Sons, Inc.
Simplified Interval Observer Scheme: A New Approach for Fault Diagnosis in Instruments
Source: MDPI AG
Robust Fault Estimation based on Interval Takagi-Sugeno Unknown Input Observer
Source: Elsevier BV
An Interval Estimator for Chlorine Monitoring in Drinking Water Distribution Systems Under Uncertain System Dynamics, Inputs and Chlorine Concentration Measurement Errors
Source: Walter de Gruyter GmbH
Interval state observer for nonlinear time varying systems
Source: Elsevier BV
LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form
Source: HAL CCSD
A New Approach to Design Interval Observers for Linear Systems
Source: Institute of Electrical and Electronics Engineers (IEEE)
Asymptotically Stable Interval Observers for Planar Systems With Complex Poles
Source: Institute of Electrical and Electronics Engineers (IEEE)
Near optimal interval observers bundle for uncertain bioreactors
Source: Elsevier BV
An effective method to interval observer design for time-varying systems
Source: Elsevier BV
State estimation of system with bounded uncertain parameters: Interval multimodel approach
Source: Wiley
State-feedback control for LPV systems with interval uncertain parameters
Source: Elsevier BV
Fuzzy identification of systems and its applications to modeling and control
Source: Institute of Electrical and Electronics Engineers (IEEE)
Systematic Multimodeling Methodology Applied to an Activated Sludge Reactor Model
Source: American Chemical Society (ACS)
Fuzzy identification of systems and its applications to modeling and control
Source: Institute of Electrical and Electronics Engineers (IEEE)
Interval State Estimation for a Class of Nonlinear Systems
Source: Institute of Electrical and Electronics Engineers (IEEE)
A New Approach to Linear Filtering and Prediction Problems
Source: ASME International
A New Approach to Linear Filtering and Prediction Problems
Source: ASME International

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.