Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables

This paper is dedicated to the problem of observer design for Takagi-Sugeno (T-S) nonlinear systems with unmeasurable premise variables (TSUPV) and application to autonomous bicycle system. The main idea is based on the use of differential mean value theorem combined to the sector nonlinearity transformation. The objective of this approach is to make the state estimation error dynamic on a T-S form which allows to apply the classical Lyapunov analysis to derive convergence conditions. The design algorithm is proposed in terms of linear matrix inequalities (LMI). To illustrate the proposed methodology, a nonlinear bicycle model is considered.

[1]  J. Ragot,et al.  Nonquadratic stability analysis of Takagi-Sugeno models , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[2]  S.T.H. Jansen,et al.  Motorcycle state estimation for lateral dynamics , 2012 .

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

[4]  Wang Zicai.  Observer Design for a Class of Nonlinear Systems , 1998 .

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

[6]  Jun Yoneyama,et al.  Hinfinity filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach , 2009, Fuzzy Sets Syst..

[7]  F Yuan,et al.  Stabilizing control design of a motorcycle , 2007 .

[8]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[9]  Rainer Palm,et al.  Observers for Takagi-Sugeno fuzzy systems , 2002, IEEE Trans. Syst. Man Cybern. Part B.

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

[11]  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.

[12]  Qing Zhao,et al.  H/sub /spl infin// observer design for lipschitz nonlinear systems , 2006, IEEE Transactions on Automatic Control.

[13]  B. M. Arx.  Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis , 2008 .

[14]  Jerrold E. Marsden,et al.  Control for an autonomous bicycle , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[15]  J. Ragot,et al.  Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model , 2007, 2007 Mediterranean Conference on Control & Automation.

[16]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[17]  José Ragot,et al.  Model structure simplification of a biological reactor , 2009 .

[18]  Sergio M. Savaresi,et al.  Attitude Estimation of a Motorcycle Via Unscented Kalman Filter , 2010 .

[19]  J. Daafouz,et al.  Parameter-dependent state observer design for affine LPV systems , 2001 .

[20]  B. Marx,et al.  Design of observers for TakagiߝSugeno descriptor systems with unknown inputs and application to fault diagnosis , 2007 .

[21]  F. Thau.  Observing the state of non-linear dynamic systems† , 1973 .

[22]  P. Bergsten,et al.  Sliding mode observer for a Takagi Sugeno fuzzy system , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[23]  C. J. Lopez-Toribio,et al.  Fuzzy observers for nonlinear dynamic systems fault diagnosis , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[24]  Yu Yao,et al.  Observer Design for Lipschitz nonlinear Systems , 2009, Control. Intell. Syst..

[25]  Thierry-Marie Guerra,et al.  Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form , 2006, Fuzzy Sets Syst..

[26]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[27]  Man Ieee Systems,et al.  IEEE transactions on systems, man and cybernetics. Part B, Cybernetics , 1996 .

[28]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[29]  J. Ragot,et al.  Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[30]  P. Bergsten,et al.  Fuzzy observers , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).