State Estimation via Observers with Unknown Inputs: Application to a Particular Class of Uncertain Takagi-Sugeno Systems

This paper deals with the design of a multiple observer allowing estimating the state vector of a nonlinear system described by a Takagi-Sugeno multiple model subject to modelling and input uncertainties which are considered as unknown inputs. The main contribution of the paper is the conception of a multiple observer based on the elimination of these unknown inputs. Convergence conditions are established in order to guarantee the convergence of the state estimation error. These conditions are expressed in Linear Matrix Inequality (LMI) formulation. An example of simulation is given to illustrate the proposed method.

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

[2]  José Ragot,et al.  Structure identification in multiple model representation: elimination and merging of local models , 2001 .

[3]  Jie Chen,et al.  Observer-based fault detection and isolation: robustness and applications , 1997 .

[4]  Mohammed Chadli,et al.  Design of robust observer for uncertain Takagi-Sugeno models , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

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

[6]  Jer-Guang Hsieh,et al.  LMI approach to design of robust state observer for uncertain systems with time-delay perturbation , 2002, 2002 IEEE International Conference on Industrial Technology, 2002. IEEE ICIT '02..

[7]  M. Saif,et al.  A novel approach to the design of unknown input observers , 1991 .

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

[9]  Dimitar Filev.  Fuzzy modeling of complex systems , 1991, Int. J. Approx. Reason..

[10]  Shaocheng Tong,et al.  Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties , 2002, Fuzzy Sets Syst..

[11]  J. Meditch,et al.  Observers for systems with unknown and inaccessible inputs , 1973, CDC 1973.

[12]  M. Benrejeb,et al.  State and sensor faults estimation via a proportional integral observer , 2009, 2009 6th International Multi-Conference on Systems, Signals and Devices.

[13]  Rodolfo Orjuela.  Contribution à l'estimation d'état et au diagnostic des systèmes représentés par des multimodèles , 2008 .

[14]  P. Dorato,et al.  Observing the states of systems with unmeasurable disturbances , 1975 .

[15]  A. Akhenak.  Conception d'observateurs non linéaires par approche multimodèle : application au diagnostic , 2004 .

[16]  J. Park,et al.  Adaptive fuzzy observer with minimal dynamic order for uncertain nonlinear systems , 2003 .