JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2016, Vol. 46 ›› Issue (3): 79-86.doi: 10.6040/j.issn.1672-3961.0.2015.394

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Stabilization and H∞ control for nonlinear switched Hamiltonian systems subject to actuator saturation

LI Han, WEI Airong*   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China
  • Received:2015-12-02 Online:2016-06-30 Published:2015-12-02

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Abstract: The stabilization and H∞ control problems of nonlinear switched Hamiltonian systems(NSHSs)subject to actuator saturation under arbitrary switching paths was investigated. The stabilization of NSHSs with actuator saturation was studied by designing suitable state feedback and deriving a sufficient condition. Then, an H∞ controller was designed to realize the H∞ control of NSHSs subject to actuator saturation with external disturbances, under the designed controller, γ-dissipation inequality held for the system with external disturbances, moreover, the globally asymptotical stabilization was achieved for the corresponding closed-loop system without external disturbances. A simulation example showed that the proposed method and results were effective.

Key words: H∞ control, stabilization, Hamiltonian systems, nonlinear switched, actuator saturation

CLC Number: 

  • TP273
[1] GE S S, LEE T H, HARRIS C J. Adaptive neural network control of robotic manipulators[M]. London, UK: World Scientific, 1998.
[2] FOSSEN T I. Marine control systems:guidance, navigation, and control of ships, rigs and underwater vehicles[M]. Trondheim, Norway:Marine Cybernetics AS, 2002.
[3] SLOTINE J E, LI W. Applied nonlinear control[M]. New Jersey, USA: Prentice Hall, 1991.
[4] BULLO F. Averaging and vibrational control of mechanical systems[J]. SIAM J Control Optimi, 2002, 41(2):542-562.
[5] XI Z, CHEND D, LU Q, et al. Nonlinear decentralized controller design for multimachine power systems using Hamiltonian function method[J]. Automatica, 2002, 38(3):527-534.
[6] SUN L, WANG Y. Stabilization and H∞ control of a class of nonlinear Hamiltonian descriptor systems with application to nonlinear descriptor systems[J]. Control Theory & Applications, 2010, 4(1):16-26.
[7] YU H, YU J, LIU X, et al. Port-Hamiltonian system modeling and position tracking control of PMSM based on maximum output power principle[J]. ICIC Express Letters, 2012, 6(1-6):437-442.
[8] WANG Y, FENG G, CHENG D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems[J]. Automatica, 2007(43):403-415.
[9] LIANG Y, MA R, WANG M, et al. Global finite-time stabilisation of a class of switched nonlinear systems[J]. International Journal of Systems Science, 2014, 46(16):2897-2904.
[10] SHE Z, XUE B. Discovering multiple Lyapunov functions for switched hybrid systems[J]. SIAM Journal on Control and Optimization, 2014, 52(5):3312-3340.
[11] SERON M M, DE DONA J A. On robust stability and set invariance of switched linear parameter varying systems[J]. 2015, 88(12):2588-2597.
[12] 朱礼营, 王玉振. 切换耗散 Hamilton 系统的稳定性研究 [J]. 中国科学(E辑), 2006, 36(6):617-630. ZHU Liying, WANG Yuzhen. Study on the stability of swithced dissipative Hamiltonian systems[J]. Science in China(Series E), 2006, 36(6):617-630.
[13] 朱礼营, 王玉振. 混杂切换 Hamilton 系统的 H∞ 控制[J]. 控制与决策, 2007, 22(8):956-960. ZHU Liying, WANG Yuzhen. H∞ control strategy for hybrid and switched Hamiltonian systems[J]. Control and Decision, 2007, 22(8):956-960.
[14] DUAN C, WU F. New results on switched linear systems with actuator saturation[J]. International Journal of Systems Science, 2016, 47(5):1008-1020.
[15] ZHANG J, DENG Z, WANG Y. Robust stability and stabilization of positive interval systems subject to actuator saturation[J]. Asian Journal of Control, 2014, 16(5):1553-1560.
[16] RAN M, WANG Q, DONG C, et al. Simultaneous anti-windup synthesis for linear systems subject to actuator saturation[J]. Journal of Systems Engineering and Electronics, 2015, 26(1):119-126.
[17] SONG G, LI T, LI Y, et al. Quantized output feedback stabilization for nonlinear discrete-time systems subject to saturating actuator[J]. Nonlinear Dynamics, 2016, 83(1-2):305-317.
[18] SUN L, WANG Y, FENG G. Control design for a class of affine nonlinear descriptor systems with actuator saturation[J]. IEEE Transactions on Automatic Control, 2015, 60(8):2195-2200.
[19] WEI A, WANG Y. Stabilization and H∞ control of nonlinear port-controlled Hamiltonian systems subject to actuator saturation[J]. Automatica, 2010, 46(12):2008-2010.
[20] WANG Y, CHENG D, LI C, et al. Dissipative Hamiltonian realization and energy-based L2-disturbance attenuation control of multimachine power systems[J]. IEEE Transactions on Automatic Control, 2003, 48(8):1428-1433.
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