Interval state estimation for uncertain polytopic systems

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.

[1]  Wei Xie,et al.  Control of non-linear switched systems with average dwell time: interval observer-based framework , 2016 .

[2]  Sabri Arik,et al.  A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks , 2013, Neural Networks.

[3]  Denis V. Efimov,et al.  Interval Observers for Time-Varying Discrete-Time Systems , 2013, IEEE Transactions on Automatic Control.

[4]  Guojian Shao,et al.  Sensitivity and inverse analysis methods for parameter intervals , 2010 .

[5]  Vicenç Puig,et al.  Robust Fault Estimation based on Interval Takagi-Sugeno Unknown Input Observer , 2018 .

[6]  Julien Marzat,et al.  Interval observer design for unknown input estimation of linear time-invariant discrete-time systems , 2017 .

[7]  Olivier Bernard,et al.  Asymptotically Stable Interval Observers for Planar Systems With Complex Poles , 2010, IEEE Transactions on Automatic Control.

[8]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[9]  David Henry,et al.  Multiobjective interval observer via LMI techniques for fault detection , 2016, 2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol).

[10]  Denis V. Efimov,et al.  An effective method to interval observer design for time-varying systems , 2014, Autom..

[11]  José Ragot,et al.  Systematic Multimodeling Methodology Applied to an Activated Sludge Reactor Model , 2010 .

[12]  B. Marx,et al.  Brief paper: state estimation of Takagi-Sugeno systems with unmeasurable premise variables , 2010 .

[13]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[14]  Damiano Rotondo,et al.  State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers , 2018, Int. J. Control.

[15]  Yan Wang,et al.  Interval observer design for LPV systems with parametric uncertainty , 2015, Autom..

[16]  Didier Maquin,et al.  State estimation of system with bounded uncertain parameters: Interval multimodel approach , 2018 .

[17]  Alfredo Germani,et al.  A New Approach to Design Interval Observers for Linear Systems , 2015, IEEE Transactions on Automatic Control.

[18]  Fanglai Zhu,et al.  State and sensor fault interval estimations for discrete-time systems , 2017, 2017 36th Chinese Control Conference (CCC).

[19]  Luigi Chisci,et al.  Recursive state bounding by parallelotopes , 1996, Autom..

[20]  Nam Kyu Kwon,et al.  State-feedback control for LPV systems with interval uncertain parameters , 2015, J. Frankl. Inst..

[21]  Mihaela-Hanako Matcovschi,et al.  Diagonal stability of interval matrices and applications , 2010 .

[22]  Y. Candau,et al.  Complex Interval Constraint Propagation for Non Linear Bounded-Error Parameter Identification , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Cuihong Wang,et al.  Positive observer for positive continuous systems with interval uncertainties and multiple time-delay , 2012, 2012 24th Chinese Control and Decision Conference (CCDC).

[24]  Ramon E. Moore.  Interval arithmetic and automatic error analysis in digital computing , 1963 .

[25]  Yamina Menasria,et al.  An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model , 2017 .

[26]  Vicenç Puig,et al.  Fault Estimation using a Takagi-Sugeno Interval Observer: Application to a PEM Fuel Cell , 2017, ICINCO.

[27]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[28]  Thierry-Marie Guerra,et al.  Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach , 2008, IEEE Transactions on Automatic Control.

[29]  Akaninyene Udo Udom.  Exponential stabilization of stochastic interval system with time dependent parameters , 2012, Eur. J. Oper. Res..

[30]  Denis V. Efimov,et al.  Interval State Estimation for a Class of Nonlinear Systems , 2012, IEEE Transactions on Automatic Control.

[31]  Andrey Polyakov,et al.  Interval observer approach to output stabilization of time-varying input delay systems , 2013, 2013 European Control Conference (ECC).

[32]  Denis V. Efimov,et al.  Design of interval observers for uncertain dynamical systems , 2016, Automation and Remote Control.

[33]  D. Luenberger.  An introduction to observers , 1971 .

[34]  Tarek Raïssi,et al.  Interval observer framework for fault-tolerant control of linear parameter-varying systems , 2018, Int. J. Control.

[35]  Yi Shen,et al.  Interval observer design for uncertain discrete-time linear systems , 2018, Syst. Control. Lett..

[36]  Anuradha Roy,et al.  Equivalency between vertices and centers-coupled-with-radii principal component analyses for interval data , 2015 .

[37]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..

[38]  Olivier Bernard,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007, 2007 European Control Conference (ECC).

[39]  Alejandro Alvarado-Lassman,et al.  Simplified Interval Observer Scheme: A New Approach for Fault Diagnosis in Instruments , 2011, Sensors.

[40]  Vicenç Puig,et al.  Fault detection and isolation using viability theory and interval observers , 2018, Int. J. Syst. Sci..

[41]  Dalil Ichalal,et al.  Interval observer for LPV systems with unknown inputs , 2017 .

[42]  Didier Dumur,et al.  Ellipsoidal state estimation for systems with interval uncertainties , 2014, 53rd IEEE Conference on Decision and Control.

[43]  Mietek A. Brdys,et al.  An Interval Estimator for Chlorine Monitoring in Drinking Water Distribution Systems Under Uncertain System Dynamics, Inputs and Chlorine Concentration Measurement Errors , 2017, Int. J. Appl. Math. Comput. Sci..

[44]  Zhi-Hui Zhang,et al.  Interval Observer-Based Fault Isolation for Discrete-Time Fuzzy Interconnected Systems With Unknown Interconnections , 2017, IEEE Transactions on Cybernetics.

[45]  Chao Wang,et al.  The normalized interval regression model with outlier detection and its real-world application to house pricing problems , 2015, Fuzzy Sets Syst..

[46]  Fanglai Zhu,et al.  Interval observer design for discrete-time switched system , 2017 .

[47]  Fanglai Zhu,et al.  Actuator fault detection and interval reconstruction based on interval observers , 2017 .

[48]  Denis V. Efimov,et al.  Interval state observer for nonlinear time varying systems , 2013, Autom..