Non-minimum phase switched systems: HOSM-based fault detection and fault identification via Volterra integral equation ‡,§

SUMMARY In this paper, the problem of continuous and discrete state estimation for a class of linear switched systems with additive faults is studied. The class of systems under study can contain non-minimum phase zeroes in some of their ‘operating modes’. The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state space is decomposed into the strongly observable part, the non-strongly observable part, and the unobservable part, to analyze the effect of the unknown inputs. State observers based on high-order sliding mode to exactly estimate the strongly observable part and Luenberger-like observers to estimate the remaining parts are proposed. For the case when the exact estimation of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The proposed strategy includes a high-order sliding-mode-based fault detection and a fault identification scheme via the solution of a Volterra integral equation. The feasibility of the proposed method is illustrated by simulations. Copyright © 2013 John Wiley & Sons, Ltd.

[1]  G.K. Fourlas,et al.  Fault Diagnosis of Hybrid Systems , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[2]  Gautam Biswas,et al.  Model-Based Diagnosis of Hybrid Systems , 2003, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Yuri B. Shtessel,et al.  HOSM Observer for a Class of Non-Minimum Phase Causal Nonlinear MIMO Systems , 2010, IEEE Transactions on Automatic Control.

[4]  Denis V. Efimov,et al.  Hybrid adaptive observers for locally Lipschitz systems with application to mechanical oscillators , 2009, 2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC).

[5]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[6]  Salim Chaib,et al.  Failure detection and reconstruction in switched nonlinear systems , 2009 .

[7]  Miguel Ayala Botto,et al.  Simultaneous state and input estimation of hybrid systems with unknown inputs , 2006, Autom..

[8]  D. Henry,et al.  Design and analysis of robust residual generators for systems under feedback control , 2005, Autom..

[9]  Ali Zolghadri,et al.  Advanced model-based FDIR techniques for aerospace systems: Today challenges and opportunities , 2012 .

[10]  Bin Jiang,et al.  Robust fault tolerant tracking control with application to hybrid nonlinear systems , 2009 .

[11]  Christopher Edwards,et al.  Nonlinear robust fault reconstruction and estimation using a sliding mode observer , 2007, Autom..

[12]  Feng Zhao,et al.  Monitoring and fault diagnosis of hybrid systems , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Alexander S. Poznyak,et al.  Observation of linear systems with unknown inputs via high-order sliding-modes , 2007, Int. J. Syst. Sci..

[14]  M. Hautus.  Strong detectability and observers , 1983 .

[15]  Daniel Liberzon,et al.  On Invertibility of Switched Linear Systems , 2006, CDC.

[16]  Michel Kinnaert,et al.  Diagnosis and Fault-Tolerant Control , 2006 .

[17]  Chee Pin Tan,et al.  Sliding mode observers for fault detection and isolation , 2002 .

[18]  Inseok Hwang,et al.  A Survey of Fault Detection, Isolation, and Reconfiguration Methods , 2010, IEEE Transactions on Control Systems Technology.

[19]  Wilfrid Perruquetti,et al.  Algebraic switching time identification for a class of linear hybrid systems , 2011 .

[20]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[21]  Wei Kang,et al.  On the Observability of Nonlinear and Switched Systems , 2009 .

[22]  Alessandro Giua,et al.  Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems , 2011 .

[23]  Donghua Zhou,et al.  Robust state estimation and fault diagnosis for uncertain hybrid nonlinear systems , 2007 .

[24]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[25]  Noureddine Manamanni,et al.  State observer and observability conditions for a class of hybrid continuous-discrete dynamic system , 2007, 2007 46th IEEE Conference on Decision and Control.

[26]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[27]  Alessandro Giua,et al.  Robust reconstruction of the discrete state for a class of nonlinear uncertain switched systems , 2011, ADHS.

[28]  A. Abdo,et al.  Design of robust fault detection filter for hybrid switched systems , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[29]  Alessandro Pisano,et al.  Finite-time converging jump observer for switched linear systems with unknown inputs ☆ , 2011 .

[30]  David Henry,et al.  Design of Robust Fault Detection Filters for Multivariable Feedback Systems , 2006 .

[31]  Inseok Hwang,et al.  Robust estimation and fault detection and isolation algorithms for stochastic linear hybrid systems with unknown fault input , 2011 .

[32]  Christopher Edwards.  Sliding mode methods for fault detection and fault tolerant control , 2012 .

[33]  Karl Henrik Johansson,et al.  Dynamical properties of hybrid automata , 2003, IEEE Trans. Autom. Control..

[34]  Leonid M. Fridman,et al.  Robust exact finite-time output based control using high-order sliding modes , 2011, Int. J. Syst. Sci..

[35]  J. Barbot,et al.  Nonlinear Observer for Autonomous Switching Systems with Jumps , 2007 .

[36]  Arie Levant,et al.  Exact Differentiation of Signals with Unbounded Higher Derivatives , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[37]  Halim Alwi,et al.  Sliding mode estimation schemes for incipient sensor faults , 2009, Autom..

[38]  Francisco Javier Bejarano,et al.  Partial unknown input reconstruction for linear systems , 2011, Autom..

[39]  Leonid Fridman,et al.  STATE OBSERVATION FOR NONLINEAR SWITCHED SYSTEMS USING NONHOMOGENEOUS HIGH-ORDER SLIDING MODE OBSERVERS , 2012 .

[40]  Arie Levant,et al.  High-order sliding-mode observation for linear systems with unknown inputs , 2011 .

[41]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[42]  Leonid M. Fridman,et al.  State estimation for linear switched systems with unstable invariant zeros and unknown inputs , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[43]  Leonid M. Fridman,et al.  High-order sliding modes observers for linear autonomous-switched systems with unknown inputs , 2012, 2012 12th International Workshop on Variable Structure Systems.

[44]  Djamel Eddine Chouaib Belkhiat,et al.  Robust Fault Detection Based-Observer for Linear Switched Systems , 2009, ADHS.

[45]  Vincent Cocquempot,et al.  Switching Time Estimation and Fault Detection for Hybrid Systems Using Structured Parity Residuals , 2003 .

[46]  V. Cocquempot,et al.  Fault detection and isolation for hybrid systems using structured parity residuals , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[47]  Alessandro Pisano,et al.  Switched Observers for Switched Linear Systems With Unknown Inputs , 2011, IEEE Transactions on Automatic Control.

[48]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[49]  Bruce Hendrickson,et al.  Support Theory for Preconditioning , 2003, SIAM J. Matrix Anal. Appl..

[50]  Inseok Hwang,et al.  Fault detection and isolation for stochastic linear hybrid systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[51]  Harry L. Trentelman,et al.  Control theory for linear systems , 2002 .

[52]  Alessandro Pisano,et al.  Continuous and Discrete State Estimation in Linear Switched Systems by Sliding Mode Observers with Residuals' Projection , 2012, ADHS.

[53]  A. Alessandri,et al.  Design of observers for switched discrete-time linear systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[54]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[55]  A. Isidori.  Nonlinear Control Systems , 1985 .

[56]  B. Molinari.  A strong controllability and observability in linear multivariable control , 1976 .

[57]  Michael Defoort,et al.  Robust finite time observer design for multicellular converters , 2011, Int. J. Syst. Sci..

[58]  Ali Zolghadri,et al.  A redundancy-based strategy for safety management in a modern civil aircraft , 2000 .