Feedback Stabilization Based on Observer and Guaranteed Cost Control for Lipschitz Nonlinear Systems
This paper presents a design of dynamic feedback
control based on observer for a class of large scale Lipschitz nonlinear
systems. The use of Differential Mean Value Theorem (DMVT) is to
introduce a general condition on the nonlinear functions. To ensure
asymptotic stability, sufficient conditions are expressed in terms of
linear matrix inequalities (LMIs). High performances are shown
through real time implementation with ARDUINO Duemilanove
board to the one-link flexible joint robot.
[1] P. Schmidt, J. Moreno, and A. Schaum, “Observer design for a class
of complex networks with unknown topoloy,” in World Congress The
International Federation of Automatic Control, August 24-29, Cape
Town, South Africa, 2014, pp. 2812–2817.
[2] H. Gripa, A. Saberi, and T. Johansenb, “Observers for interconnected
nonlinear and linear systems,” Autmatica, vol. 48, p. 13391346, 2012.
[3] C. Kravaris and C. Chung, “Nonlinear state feedback synthesis by global
input/output linearization,” AIChE J., vol. 33 (4), pp. 592–603, 1987.
[4] A. Teel and L. Praly, “Tools for smiglobal stabilization by partial
state and output feedback,” SIAM J. Control Optim., vol. 33 (5), pp.
1443–1488, 1995.
[5] U. Cem and P. Kachroo, “Sliding mode measurement feedback control
for antilock braking systems,” IEEE Trans. on Control. Syst. Technology,
vol. 7 (2), pp. 271–281, 1999.
[6] A. Rodriguez and H. Nijmeijer, “Mutual synchronization of robots via
estimated state feedback: A cooperative approach,” IEEE Trans. on
Control. Syst. Technology, vol. 12 (4), pp. 542–554, 2004.
[7] Y. Li, T. Zheng, and Y. Li, “Extended state observer based
adaptive back-stepping sliding mode control of electronic throttle in
transportation cyber-physical systems,” Mathematical Problems in Eng.,
vol. doi:10.1155/2015/301656, pp. 1–11, 2015.
[8] L. Ghaoui, F. Oustry, and M. AItRami, “A cone complementarity
linearization algorithm for static output-feedback and related problems,”
IEEE Trans. on Autom. Control, vol. 42 (8), pp. 1171–1176, 1997.
[9] D. Fernandes, A. Sorensen, K. Pettersen, and D. Donha, “Output
feedback motion control system for observation class rovs based on a
high-gain state observer: Theoretical and experimental results,” Control
Eng. Practice, vol. 39, pp. 90–102, 2015.
[10] B. Yao and M. Tomizuka, “Adaptive robust control of mimo nonlinear
systems in semi-strict feedback forms,” Autmatica, vol. 37 (9), pp.
1305–1321, 2001.
[11] H. Khalil, “High-gain observers in nonlinear feedback control,” in Int.
Conf. Control, Automation and Syst., Oct. 14-17, COEX, Seoul, Korea,
2008, pp. –.
[12] H. Khalil and L. Praly, “High-gain observer in nonlinear feedback
control,” Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/rnc.3051,
pp. –, 2013.
[13] J. Yao, Z. Jiao, and D. Ma, “Extended state observer based
output feedback nonlinear robust control of hydraulic systems with
backstepping,” IEEE Trans. on Industrial Electronics, vol. 61 (11), pp.
6285–6293, 2014.
[14] H. Liu, T. Zhang, and X. Tian, “Continuous output-fedback finite time
control for a class of second-order nonlinear systems with disturbances,”
Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/mc.3305, p. , 2015.
[15] S. Ge, C. Hang, and T. Zhang, “Adaptive neural network control of
nonlinear systems by state and output feedback,” IEEE Trans. on Syst.
Man and Cybernetics, vol. 29 (6), pp. 818–828, 1999.
[16] S. He, “Non fragile passive controller design for nonlinear markovian
jumping systems via obserber-based control,” Neurocomputing, vol. 147,
pp. 350–357, 2015.
[17] A. Zemouch and M. Boutayeb, “A unified H∞ adaptive observer
synthesis method for a class of systems with both lipschitz and monotone
nonlinearities,” Syst. Control Letters, vol. 58, pp. 282–288, 2009.
[18] A. Zemouch, M. Boutayeb, and G. Bara, “Observers for a class of
lipschitz systems with extension to H∞ performance analysis,” Syst.
Control Letters, vol. 57, pp. 18–27, 2008.
[19] A. Zemouch and M. Boutayeb, “On lmi conditions to design observers
for lipschitz nonlinear systems,” Autmatica, vol. 49, pp. 585–591, 2013.
[20] N. Gasmi, A. Thabet, M. Boutayeb, and M. Aoun, “Observer design for a
class of nonlinear discrete time systems,” in IEEE Int. Conf. on Sciences
and Techniques of Automatic Control and Computer Engineering, Dec.
21-23, Monastir, Tunisia, 2015, pp. 799–804.
[21] G. Yang, J. Wang, and Y. Soh, “Reliable guaranteed cost control for
uncertain nonlinear systems,” IEEE Trans. on Autom. Control, vol. 45,
pp. 2188–3192, 2000.
[22] S. Boyd, L. E. Ghaoui, E. Ferron, and V. Balakrishnan, Linear matrix
inequalities in systems and control theory, 15th ed. Philadelphia:
Studies in Applied Mathematics SIAM, 1994.
[23] M. Spong, “Modeling and control of elastic joint robots,” Trans. ASME,
J. Dyn. Syst., Meas. Control, vol. 109, pp. 310–319, 1987.
[1] P. Schmidt, J. Moreno, and A. Schaum, “Observer design for a class
of complex networks with unknown topoloy,” in World Congress The
International Federation of Automatic Control, August 24-29, Cape
Town, South Africa, 2014, pp. 2812–2817.
[2] H. Gripa, A. Saberi, and T. Johansenb, “Observers for interconnected
nonlinear and linear systems,” Autmatica, vol. 48, p. 13391346, 2012.
[3] C. Kravaris and C. Chung, “Nonlinear state feedback synthesis by global
input/output linearization,” AIChE J., vol. 33 (4), pp. 592–603, 1987.
[4] A. Teel and L. Praly, “Tools for smiglobal stabilization by partial
state and output feedback,” SIAM J. Control Optim., vol. 33 (5), pp.
1443–1488, 1995.
[5] U. Cem and P. Kachroo, “Sliding mode measurement feedback control
for antilock braking systems,” IEEE Trans. on Control. Syst. Technology,
vol. 7 (2), pp. 271–281, 1999.
[6] A. Rodriguez and H. Nijmeijer, “Mutual synchronization of robots via
estimated state feedback: A cooperative approach,” IEEE Trans. on
Control. Syst. Technology, vol. 12 (4), pp. 542–554, 2004.
[7] Y. Li, T. Zheng, and Y. Li, “Extended state observer based
adaptive back-stepping sliding mode control of electronic throttle in
transportation cyber-physical systems,” Mathematical Problems in Eng.,
vol. doi:10.1155/2015/301656, pp. 1–11, 2015.
[8] L. Ghaoui, F. Oustry, and M. AItRami, “A cone complementarity
linearization algorithm for static output-feedback and related problems,”
IEEE Trans. on Autom. Control, vol. 42 (8), pp. 1171–1176, 1997.
[9] D. Fernandes, A. Sorensen, K. Pettersen, and D. Donha, “Output
feedback motion control system for observation class rovs based on a
high-gain state observer: Theoretical and experimental results,” Control
Eng. Practice, vol. 39, pp. 90–102, 2015.
[10] B. Yao and M. Tomizuka, “Adaptive robust control of mimo nonlinear
systems in semi-strict feedback forms,” Autmatica, vol. 37 (9), pp.
1305–1321, 2001.
[11] H. Khalil, “High-gain observers in nonlinear feedback control,” in Int.
Conf. Control, Automation and Syst., Oct. 14-17, COEX, Seoul, Korea,
2008, pp. –.
[12] H. Khalil and L. Praly, “High-gain observer in nonlinear feedback
control,” Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/rnc.3051,
pp. –, 2013.
[13] J. Yao, Z. Jiao, and D. Ma, “Extended state observer based
output feedback nonlinear robust control of hydraulic systems with
backstepping,” IEEE Trans. on Industrial Electronics, vol. 61 (11), pp.
6285–6293, 2014.
[14] H. Liu, T. Zhang, and X. Tian, “Continuous output-fedback finite time
control for a class of second-order nonlinear systems with disturbances,”
Int. J. of Robust. Nonlinear Control, vol. doi:10.1002/mc.3305, p. , 2015.
[15] S. Ge, C. Hang, and T. Zhang, “Adaptive neural network control of
nonlinear systems by state and output feedback,” IEEE Trans. on Syst.
Man and Cybernetics, vol. 29 (6), pp. 818–828, 1999.
[16] S. He, “Non fragile passive controller design for nonlinear markovian
jumping systems via obserber-based control,” Neurocomputing, vol. 147,
pp. 350–357, 2015.
[17] A. Zemouch and M. Boutayeb, “A unified H∞ adaptive observer
synthesis method for a class of systems with both lipschitz and monotone
nonlinearities,” Syst. Control Letters, vol. 58, pp. 282–288, 2009.
[18] A. Zemouch, M. Boutayeb, and G. Bara, “Observers for a class of
lipschitz systems with extension to H∞ performance analysis,” Syst.
Control Letters, vol. 57, pp. 18–27, 2008.
[19] A. Zemouch and M. Boutayeb, “On lmi conditions to design observers
for lipschitz nonlinear systems,” Autmatica, vol. 49, pp. 585–591, 2013.
[20] N. Gasmi, A. Thabet, M. Boutayeb, and M. Aoun, “Observer design for a
class of nonlinear discrete time systems,” in IEEE Int. Conf. on Sciences
and Techniques of Automatic Control and Computer Engineering, Dec.
21-23, Monastir, Tunisia, 2015, pp. 799–804.
[21] G. Yang, J. Wang, and Y. Soh, “Reliable guaranteed cost control for
uncertain nonlinear systems,” IEEE Trans. on Autom. Control, vol. 45,
pp. 2188–3192, 2000.
[22] S. Boyd, L. E. Ghaoui, E. Ferron, and V. Balakrishnan, Linear matrix
inequalities in systems and control theory, 15th ed. Philadelphia:
Studies in Applied Mathematics SIAM, 1994.
[23] M. Spong, “Modeling and control of elastic joint robots,” Trans. ASME,
J. Dyn. Syst., Meas. Control, vol. 109, pp. 310–319, 1987.
@article{"International Journal of Information, Control and Computer Sciences:74040", author = "A. Thabet and G. B. H. Frej and M. Boutayeb", title = "Feedback Stabilization Based on Observer and Guaranteed Cost Control for Lipschitz Nonlinear Systems", abstract = "This paper presents a design of dynamic feedback
control based on observer for a class of large scale Lipschitz nonlinear
systems. The use of Differential Mean Value Theorem (DMVT) is to
introduce a general condition on the nonlinear functions. To ensure
asymptotic stability, sufficient conditions are expressed in terms of
linear matrix inequalities (LMIs). High performances are shown
through real time implementation with ARDUINO Duemilanove
board to the one-link flexible joint robot.", keywords = "Feedback stabilization, DMVT, Lipschitz nonlinear
systems, nonlinear observer, real time implementation.", volume = "10", number = "7", pages = "1395-5", }
