Robust interval observer for switched systems with unknown inputs: Application to vehicle dynamics estimation

Abstract This paper investigates the problem of robust state estimation and unknown input interval reconstruction for uncertain switched linear systems. Parameters uncertainty are supposed to be provided with known bounded compact set. A design method for obtaining interval observers that provide guaranteed lower and upper bounds of the state and unknown inputs is proposed. By adopting multiple quadratic ISS-Lyapunov function and average dwell time concept, new and less conservative stability conditions are derived, and a set of numerical feasible linear matrix inequalities (LMIs) are given. An application to vehicle lateral dynamics estimation is considered to show the effectiveness of the algorithms. Experimental data obtained with a prototype vehicle are used to confirm the performance of the proposed approach.

[1]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[2]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

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

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

[5]  Leonid M. Fridman,et al.  Interval estimation for LPV systems applying high order sliding mode techniques , 2012, Autom..

[6]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  S. Glaser,et al.  Vehicle lateral dynamics estimation using unknown input proportional-integral observers , 2006, 2006 American Control Conference.

[8]  Daniel Liberzon,et al.  Lie-Algebraic Stability Criteria for Switched Systems , 2001, SIAM J. Control. Optim..

[9]  Chenxiao Cai,et al.  Stability analysis and stabilization synthesis of singularly perturbed switched systems: An average dwell time approach , 2016 .

[10]  Tarek Raïssi,et al.  Interval observers design for continuous-time linear switched systems , 2017 .

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

[12]  Stefan Pettersson.  Designing switched observers for switched Systems using Multiple Lyapunov Functions and dwell-Time switching , 2006, ADHS.

[13]  Debasish Chatterjee,et al.  Input-to-state stability of switched systems and switching adaptive control , 2007, Autom..

[14]  Leonid M. Fridman,et al.  State Estimation for Linear Switched Systems with Unknown Inputs , 2012, ADHS.

[15]  M. Darouach,et al.  Reduced-order observer design for descriptor systems with unknown inputs , 1996, IEEE Trans. Autom. Control..

[16]  Michael Defoort,et al.  Hybrid sliding mode observer for switched linear systems with unknown inputs , 2014, J. Frankl. Inst..

[17]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..

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

[19]  Junqi Yang,et al.  Robust Full-Order and Reduced-Order Observers for a Class of Uncertain Switched Systems , 2016 .

[20]  R. Penrose.  A Generalized inverse for matrices , 1955 .

[21]  Saïd Mammar,et al.  Robust estimation of vehicle lateral velocity and yaw rate using switched T-S fuzzy interval observers , 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

[22]  R. W. Wilde,et al.  Observers for linear systems with unknown inputs , 1988 .

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

[24]  Review of Nonnegative Matrices , 1990 .

[25]  Daniel Liberzon,et al.  Input/output-to-state stability and state-norm estimators for switched nonlinear systems , 2012, Autom..

[26]  Stefen Hui,et al.  Sliding-mode observers for systems with unknown inputs: A high-gain approach , 2010, Autom..

[27]  Dalil Ichalal,et al.  Guaranteed state and unknown input estimations for linear time-invariant systems with direct feedthrough using interval observers , 2017, 2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

[28]  A. Michel,et al.  PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME , 2000 .

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

[30]  Tarek Raïssi,et al.  A note on interval observer design for unknown input estimation , 2016, Int. J. Control.

[31]  Michael Schönlein,et al.  Estimation of linear positive systems with unknown time-varying delays , 2013, Eur. J. Control.

[32]  D. Henry,et al.  Unknown input interval observer with H∞ and D-stability performance , 2017 .

[33]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

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

[35]  K. Narendra,et al.  On the stability and existence of common Lyapunov functions for stable linear switching systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[36]  Jean-Pierre Richard,et al.  Interval Estimation for Linear Switched System , 2017 .

[37]  Saïd Mammar,et al.  Synchronous interval observer design for switched LPV systems using multiple quadratic ISS-Lyapunov functions , 2017, 2017 25th Mediterranean Conference on Control and Automation (MED).

[38]  Franco Blanchini,et al.  Switched Positive Linear Systems , 2015, Found. Trends Syst. Control..

[39]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

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

[41]  Sara Ifqir,et al.  Interval observer for LPV systems: Application to vehicle lateral dynamics , 2017 .

[42]  Chun Hung Cheng,et al.  Tight robust interval observers: An LP approach , 2008, 2008 47th IEEE Conference on Decision and Control.

[43]  Rajesh Rajamani,et al.  Vehicle dynamics and control , 2005 .

[44]  Wei Zhang,et al.  State estimation with unknown input and measurement disturbance reconstruction based on descriptor systems , 2014, 53rd IEEE Conference on Decision and Control.

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