Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems
This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.
[1] O. G. Bastin and M. R. Gevers, Stable adaptive observers for nonlinear
time-varying systems, IEEE Trans. on Automatic Control, 33 (1988) pp.
650-658.
[2] R. Marino, Adaptive observers for single output nonlinear systems,
IEEE Trans. on Automatic Control, 35 (1990) 1054-1058.
[3] R. Marino and P. Tomei, Global adaptive observers for nonlinear
systems via filtered transformations, IEEE Trans. on Automatic Control,
37 (1992) 1239-1245.
[4] R. Marino, and P. Tomei, Adaptive observers with arbitrary exponential
rate of convergence for nonlinear systems, IEEE Trans. Automatic
Control, 40 (1995) 1300-1304.
[5] R. Rajamani and J. K. Hedrick, Adaptive observers for active
automotive suspensions: Theory and experiment, IEEE Trans. on
Control Systems Technology, 3 (1995) 86-93.
[6] Y. M. Cho, R. Rajamani, A systematic approach to adaptive observer
synthesis for nonlinear systems, IEEE Trans. Autom. Control. 42 (1997)
534-537.
[7] R. Marino, G. L. Santosuosso, and P. Tomei, Robust adaptive observers
for nonlinear systems with bounded disturbances, IEEE Trans. on
Automatic Control, 46 (2001) 967-972.
[8] J. Jung, K. Hul, H.K. Fathy and J.L. Srein, Optimal robust adaptive
observer design for a class of nonlinear systems via an H-infinity
approach, American Control Conf., 2006, 3637-3642.
[9] M. Hasegawa, Robust adaptive observer design based on ╬│-Positive real
problem for sensorless Induction-Motor drives, IEEE Trans. on
Industrial Electronics, 53 (2006) 76-85.
[10] A. Zemouche, M. Boutayeb, G. I. Bara, Observers for a class of
Lipschitz systems with extension to performance analysis, Systems &
Control Letters, 57 (2008) 18-27.
[11] C. S. Jeong, E. E. Yaz, A. Bahakeem, Y. I. Yaz, Resilient design of
observers with general criteria using LMIs, Proc. of ACC, 2006, 111-
116.
[12] L.H., Keel, and S.P. Bhattacharyya, Robust, fragile, or optimal?, IEEE -
Trans. Autom. Control, 42 (1997) 1098-1105.
[13] P. Dorato., non-fragile contoller design: an overview, Proc. ofACC,
1998, 2829-2831.
[14] D. Famulara, C. T. Abdallah, A. Jadbabaie, P. Domto, and W. H.
Haddad, Robust non-fragile LQ controllers: the statis feekback case",
Proc. of ACC, 1998, 1109-1113.
[15] G.H. yang, J.L. Wang, Robust nonfragile Kalman filtering for uncertain
linear systems, IEEE Trans. on Automatic Control, 46 (2001) 343-348.
[16] C. S. Jeong, E. E. Yaz, and Y. I. Yaz, Lyapunov-Based design of
resilient observers for a class of nonlinear systems and general
performance criteria, IEEE Multi-conference on Systems and Control,
2008, 942-947.
[17] C. S. Jeong, E. E. Yaz, and Y. I. Yaz , Stochastically resilient design of
H∞ observers for discrete-time nonlinear systems, IEEE Conf. CDC,
2007, 1227- 1232.
[18] F. Chen and W. Zhang, LMI criteria for robust chaos synchronization of
a class of chaotic systems, Nonlinear Analysis, 67 (2007) 3384-3393.
[19] M. Krstic, I. Kanellakopoulos, P. Kokotovic, Nonlinear and Adaptive
Control Design, John Wiley and Sons, 1995.
[20] J. Lofberg, YALMIP: A toolbox for modeling and optimization in
MATLAB, IEEE Int. Symp. Computer Aided Contol Syst. Design
Conf., 2004, 284-289.
[21] P. Gahinet, A. Nemirovski, A. Laub, M. Chilai, LMI control toolbox
user-s guide, Massachusetts: The Mathworks, 1995.
[1] O. G. Bastin and M. R. Gevers, Stable adaptive observers for nonlinear
time-varying systems, IEEE Trans. on Automatic Control, 33 (1988) pp.
650-658.
[2] R. Marino, Adaptive observers for single output nonlinear systems,
IEEE Trans. on Automatic Control, 35 (1990) 1054-1058.
[3] R. Marino and P. Tomei, Global adaptive observers for nonlinear
systems via filtered transformations, IEEE Trans. on Automatic Control,
37 (1992) 1239-1245.
[4] R. Marino, and P. Tomei, Adaptive observers with arbitrary exponential
rate of convergence for nonlinear systems, IEEE Trans. Automatic
Control, 40 (1995) 1300-1304.
[5] R. Rajamani and J. K. Hedrick, Adaptive observers for active
automotive suspensions: Theory and experiment, IEEE Trans. on
Control Systems Technology, 3 (1995) 86-93.
[6] Y. M. Cho, R. Rajamani, A systematic approach to adaptive observer
synthesis for nonlinear systems, IEEE Trans. Autom. Control. 42 (1997)
534-537.
[7] R. Marino, G. L. Santosuosso, and P. Tomei, Robust adaptive observers
for nonlinear systems with bounded disturbances, IEEE Trans. on
Automatic Control, 46 (2001) 967-972.
[8] J. Jung, K. Hul, H.K. Fathy and J.L. Srein, Optimal robust adaptive
observer design for a class of nonlinear systems via an H-infinity
approach, American Control Conf., 2006, 3637-3642.
[9] M. Hasegawa, Robust adaptive observer design based on ╬│-Positive real
problem for sensorless Induction-Motor drives, IEEE Trans. on
Industrial Electronics, 53 (2006) 76-85.
[10] A. Zemouche, M. Boutayeb, G. I. Bara, Observers for a class of
Lipschitz systems with extension to performance analysis, Systems &
Control Letters, 57 (2008) 18-27.
[11] C. S. Jeong, E. E. Yaz, A. Bahakeem, Y. I. Yaz, Resilient design of
observers with general criteria using LMIs, Proc. of ACC, 2006, 111-
116.
[12] L.H., Keel, and S.P. Bhattacharyya, Robust, fragile, or optimal?, IEEE -
Trans. Autom. Control, 42 (1997) 1098-1105.
[13] P. Dorato., non-fragile contoller design: an overview, Proc. ofACC,
1998, 2829-2831.
[14] D. Famulara, C. T. Abdallah, A. Jadbabaie, P. Domto, and W. H.
Haddad, Robust non-fragile LQ controllers: the statis feekback case",
Proc. of ACC, 1998, 1109-1113.
[15] G.H. yang, J.L. Wang, Robust nonfragile Kalman filtering for uncertain
linear systems, IEEE Trans. on Automatic Control, 46 (2001) 343-348.
[16] C. S. Jeong, E. E. Yaz, and Y. I. Yaz, Lyapunov-Based design of
resilient observers for a class of nonlinear systems and general
performance criteria, IEEE Multi-conference on Systems and Control,
2008, 942-947.
[17] C. S. Jeong, E. E. Yaz, and Y. I. Yaz , Stochastically resilient design of
H∞ observers for discrete-time nonlinear systems, IEEE Conf. CDC,
2007, 1227- 1232.
[18] F. Chen and W. Zhang, LMI criteria for robust chaos synchronization of
a class of chaotic systems, Nonlinear Analysis, 67 (2007) 3384-3393.
[19] M. Krstic, I. Kanellakopoulos, P. Kokotovic, Nonlinear and Adaptive
Control Design, John Wiley and Sons, 1995.
[20] J. Lofberg, YALMIP: A toolbox for modeling and optimization in
MATLAB, IEEE Int. Symp. Computer Aided Contol Syst. Design
Conf., 2004, 284-289.
[21] P. Gahinet, A. Nemirovski, A. Laub, M. Chilai, LMI control toolbox
user-s guide, Massachusetts: The Mathworks, 1995.
@article{"International Journal of Information, Control and Computer Sciences:54928", author = "M. Pourgholi and V.J.Majd", title = "Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems", abstract = "This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.
", keywords = "Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.", volume = "6", number = "3", pages = "332-5", }
