State estimation of system with bounded uncertain parameters: Interval multimodel approach

The objective of this study is the analysis of dynamic systems represented by multi-model with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires to consider all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment. This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger type observer, fed with the system measurements.

[1]  Damiano Rotondo,et al.  Robust fault diagnosis of proton exchange membrane fuel cells using a Takagi-Sugeno interval observer approach , 2016 .

[2]  Alain Vande Wouwer,et al.  Continuous-discrete confidence interval observer - Application to vehicle positioning , 2013, Inf. Fusion.

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

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

[5]  Denis V. Efimov,et al.  Interval observers for continuous-time LPV systems with L1/L2 performance , 2015, Autom..

[6]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[7]  Mietek A. Brdys,et al.  Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator , 2007, Int. J. Appl. Math. Comput. Sci..

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

[9]  J. Lam,et al.  Positive state-bounding observer for interval positive systems under L1 performance , 2014, Proceedings of the 33rd Chinese Control Conference.

[10]  Tarek Raïssi.  Méthodes ensemblistes pour l'estimation d'état et de paramètres , 2004 .

[11]  Xiao Wei Yang,et al.  Interval eigenvalue analysis for structures with interval parameters , 2003 .

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

[13]  C. Combastel.  A State Bounding Observer for Uncertain Non-linear Continuous-time Systems based on Zonotopes , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Thierry-Marie Guerra,et al.  Continuous Takagi–Sugeno's Models: Reduction of the Number of LMI Conditions in Various Fuzzy Control Design Technics , 2007, IEEE Transactions on Fuzzy Systems.

[15]  Luc Jaulin,et al.  Nonlinear bounded-error state estimation of continuous-time systems , 2002, Autom..

[16]  A. Vande Wouwer,et al.  Improving continuous–discrete interval observers with application to microalgae-based bioprocesses , 2009 .

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

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

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

[20]  M. Ait Rami,et al.  Robust interval observer with uncertainties in the output , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[21]  Pierre Apkarian,et al.  Overview of linear time-invariant interval observer design: towards a non-smooth optimisation-based approach , 2016 .

[22]  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.

[23]  Tarek Raïssi,et al.  Interval observer design for Linear Parameter-Varying systems subject to component faults , 2016, 2016 24th Mediterranean Conference on Control and Automation (MED).

[24]  James Lam,et al.  Positive Observers and Dynamic Output-Feedback Controllers for Interval Positive Linear Systems , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[26]  A. Zolghadri,et al.  Interval State and Unknown Inputs Estimation for Linear Time-Invariant Systems , 2014 .

[27]  Jean-Luc Gouzé,et al.  Near optimal interval observers bundle for uncertain bioreactors , 2007 .

[28]  A I Bulgakov,et al.  Approximation of differential inclusions , 2002 .

[29]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[30]  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..

[31]  Kevin L. Moore,et al.  Stability analysis of discrete-time iterative learning control systems with interval uncertainty , 2007, Autom..

[32]  Pravin Varaiya,et al.  Epsilon-Approximation of Differential Inclusions , 1996, Hybrid Systems.

[33]  Lev V. Utkin,et al.  A new robust model of one-class classification by interval-valued training data using the triangular kernel , 2015, Neural Networks.

[34]  J. Ragot,et al.  Evaluation des bornes de l'état d'un système incertain. Approche par intervalles , 2003 .

[35]  Wilfrid Perruquetti,et al.  On interval observer design for time-invariant discrete-time systems , 2013, 2013 European Control Conference (ECC).

[36]  David Henry,et al.  Unknown input interval observer for uncertain linear time invariant systems , 2016, 2016 UKACC 11th International Conference on Control (CONTROL).

[37]  Jean-Luc Gouzé,et al.  Closed loop observers bundle for uncertain biotechnological models , 2004 .

[38]  Frédéric Mazenc,et al.  Interval observer composed of observers for nonlinear systems , 2014, 2014 European Control Conference (ECC).

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

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