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Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

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Języki publikacji
EN
Abstrakty
EN
This paper investigates the problem of adaptive robust simultaneous stabilization (ARSS) of two dissipative Hamiltonian systems (DHSs), and proposes a number of results on the controller parameterization design. Firstly, an adaptive H control design approach is presented by using the dissipative Hamiltonian structural for the case that there are both external disturbances and parametric uncertainties in two DHSs. Secondly, an algorithm for solving tuning parameters of the controller is proposed using symbolic computation. The proposed controller parameterization method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Finally, an illustrative example is presented to show that the ARSS controller obtained in this paper works very well.
Rocznik
Strony
505--525
Opis fizyczny
Bibliogr. 24 poz., wykr., wzory
Twórcy
autor
  • School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China
  • Guangdong Provincial Engineering and Tech- nology Research Center for Mathematical Education Software, Guangzhou, 510006, China
autor
  • School of Energy Science and Engineering, University of Electronic Science and Technology of China 611731, Chengdu, China,
autor
  • Lab Center, Guangzhou University, Guangzhou 510006, China
Bibliografia
  • [1] G. D. Howitt and R. Luus: Simultaneous stabilization of linear single-input systems by linear state feedback control. Int. J. of Control, 54(4), (1991), 1015-1030.
  • [2] M. Paskota, V. Sreeram, K. L. Teo and A. I. Mees: Optimal simultaneous stabilization of linear single-input systems via linear state feedback control. Int. J. of Control, 60(4), (1994), 483-498.
  • [3] D. Miller and D Kennedy: Simultaneous stabilization with near-optimal model reference tracking. Systems & Control Letters, 46(1), (2002), 31-43.
  • [4] X. Wang, A. Saberi, A. A. Stoorvogel and P. Sannuti: Simultaneous global external and internal stabilization of linear time-invariant discrete-time systems subject to actuator saturation. Automatica, 48(5), (2012), 699-711.
  • [5] B. Ho-Mock-Qai and W.P. Dayawansa: Simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback. SIAM J. on Control and Optimization, 37(6), (1999), 1701-1725.
  • [6] J. L. Wu: Simultaneous stabilization for a collection of single-input nonlinear systems. IEEE Trans. on Automatic Control, 50(3), (2005), 328-337.
  • [7] J. Xu, L. Xie and Y. Wang: Simultaneous stabilization and robust control of polynomial nonlinear systems using SOS techniques. IEEE Trans. on Automatic Control, 54(8), (2009), 1892-1897.
  • [8] Y. Wang, G. Feng and D. Cheng: Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica, 43(3), (2007), 403-415.
  • [9] L. Sun and Y. Wang: Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method. Science in China Series F: Information Sciences, 52(11), (2009), 2140-2152.
  • [10] A. Wei, Y. Wang and X. Hu: Parallel simultaneous stabilization of a set of port-controlled Hamiltonian systems subject to actuator saturation. J. of Systems Science and Complexity, 24(1), (2011), 120-139.
  • [11] A. Wei, Y. Wang and X. Hu: Adaptive robust parallel simultaneous stabilization of two uncertain port-controlled Hamiltonian systems subject to input saturation. The 31st Chinese Control Conf. (CCC), (2012), 727-732.
  • [12] D. C. Youla, H. Jabr and J. J. Bongiorno Jr: Modern Wiener-Hopf design of optimal controllers, Part II: The multivariable case. IEEE Trans. on Automatic Control, 21 (1976), 319-338.
  • [13] W. M. Lu and J. C. Doyle: Control of nonlinear systems via output feedback: controller parameterization. IEEE Trans. on Automatic Control, 39(12), (1994), 2517-2521.
  • [14] C. F. Yung, J. L. Wu and T. T. Lee: Parameterization of nonlinear H∞ state-feedback controllers. Automatica, 33(8), (1997), 1587-1590.
  • [15] Y. S. Fu, Z. H. Tian, and S. J. Shi: A family of reliable H∞ state-feedback controllers for nonlinear systems with strictly redundant actuators: the full information case. J. of Systems Science and Systems Engineering, 10(3), (2001), 350-358.
  • [16] J. Gadewadikar, F. L. Lewis, L. Xie, V. Kucera and M. Abu-Khalaf: Parameterization of all stabilizing H∞ static state-feedback gains: Application to output-feedback design. Automatica, 43(9), (2007), 1597-1604.
  • [17] S. Xu and X. Hou: A family of H∞ controllers for dissipative Hamiltonian systems. Int. J. of Robust and Nonlinear Control, 22(11), (2012), 1258-1269.
  • [18] Z. Cao and X. Hou: A Symbolic computation approach to parameterizing controller for polynomial Hamiltonian systems. Mathematical Problems in Engineering, Article ID 806428, (2014).
  • [19] T. Shen: H∞ Control Theory and its Applications. Tsinghua University Press, Beijing, 1996.
  • [20] A. Van der Schaft: L2-Gain and Passivity Techniques in Nonlinear Control. Springer, Berlin, 2012.
  • [21] Y. Wang, D. Chen, C. Li and Y. Ge: Dissipative Hamiltonian realization and energy-based L2-disturbance attenuation control of multimachine power systems. IEEE Trans. on Automatic Control, 48(8), (2003), 1428-1433.
  • [22] Y. Wang, D. Chen and S. Ge: Approximate dissipative Hamiltonian realization and construction of local Lyapunov function. Systems & Control Letters, 56(2), (2007), 141-149.
  • [23] B. F. Caviness and J. R. Johnson: Quantifier elimination and cylindrical algebraic decomposition. Springer Science & Business Media, 1998.
  • [24] K. N. Swamy: On Sylvesters criterion for positive-semidefinite matrices. IEEE Trans. on Automatic Control, 18(3), (1973), 306.
Uwagi
EN
This work was supported by the National Natural Science Foundation of China No. 61374001, National High Technology Research and Development Program of China No. 2015AA015408 and the scholarship from China Scholarship Council (CSC) under the Grant CSC No. 201609945011.
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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Bibliografia
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