A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

Authors

Abstract

This paper investigates the robust simultaneous stabilization (RSS) and robust adaptive simultaneous stabilization (RASS) problem for a set of port‐controlled Hamiltonian (PCH) systems. Some results for designing a family of robust simultaneous controllers with tuning parameters for such systems are proposed. Firstly, using the dissipative Hamiltonian structural properties, these systems are combined to generate an augmented PCH system, and two simultaneous stabilization controllers with parameters are designed for the systems: one is a robust controller and the other is adaptive. Secondly, an algorithm for solving the tuning parameters’ ranges of controller is proposed with symbolic computation. Finally, a numerical example is studied by applying the method obtained in this paper to a set of PCH systems with external disturbance. The effectiveness of the proposed control method is verified by simulations. Compared with conventional simultaneous stabilization control, the controller obtained in this paper not only has strong robustness for a set of systems, but also can optimize the robustness for the systems by adjusting the parameters’ values.

Citation

Journal: Asian Journal of Control
Year: 2017
Volume: 19
Issue: 1
Pages: 151–163
Publisher: Wiley
DOI: 10.1002/asjc.1341

BibTeX

@article{Cao_2016,
  title={{A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems}},
  volume={19},
  ISSN={1934-6093},
  DOI={10.1002/asjc.1341},
  number={1},
  journal={Asian Journal of Control},
  publisher={Wiley},
  author={Cao, Zhong and Hou, Xiaorong and Zhao, Wenjing},
  year={2016},
  pages={151--163}
}

Download the bib file

References

Doyle, J. C., Glover, K., Khargonekar, P. P. & Francis, B. A. State-space solutions to standard H/sub 2/ and H/sub infinity / control problems. IEEE Trans. Automat. Contr. 34, 831–847 (1989) – 10.1109/9.29425
Isidori, A. & Astolfi, A. Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems. IEEE Trans. Automat. Contr. 37, 1283–1293 (1992) – 10.1109/9.159566
Lu W. M., H ∞ control of nonlinear systems via output feedback: controller parameterization. IEEE Trans. Autom. Control (1994)
Chee-Fai Yung, Yung-Pin Lin & Fang-Bo Yeh. A family of nonlinear H/sup ∞/-output feedback controllers. IEEE Trans. Automat. Contr. 41, 232–236 (1996) – 10.1109/9.481524
Fu Y. S., A family of reliable nonlinear H ∞ state‐feedback controllers. IET Control Theory Appl. (2001)
Feng, Y., Yagoubi, M. & Chevrel, P. Parametrization of extended stabilizing controllers for continuous-time descriptor systems. Journal of the Franklin Institute 348, 2633–2646 (2011) – 10.1016/j.jfranklin.2011.08.006
Xu, S. & Hou, X.-R. A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems. Int. J. Autom. Comput. 8, 209–214 (2011) – 10.1007/s11633-011-0575-3
Xu, S. & Hou, X. A family of H∞ controllers for dissipative Hamiltonian systems. Intl J Robust & Nonlinear 22, 1258–1269 (2011) – 10.1002/rnc.1753
Cai, W., Fan, L. & Song, Y. Robust Adaptive Fault-Tolerant Control of Stochastic Systems with Modeling Uncertainties and Actuator Failures. Abstract and Applied Analysis 2014, 1–11 (2014) – 10.1155/2014/450521
Saadatjoo, F., Derhami, V. & Karbassi, S. M. Simultaneous control of linear systems by state feedback. Computers & Mathematics with Applications 58, 154–160 (2009) – 10.1016/j.camwa.2009.01.039
Xiao, N., Xie, L. & Fu, M. Stabilization of Markov jump linear systems using quantized state feedback. Automatica 46, 1696–1702 (2010) – 10.1016/j.automatica.2010.06.018
Gündeş, A. N. Simultaneous and strong simultaneous stabilisation of some classes of MIMO systems. International Journal of Control 84, 1171–1182 (2011) – 10.1080/00207179.2011.594907
Yu, T. & Chi, W. Sufficient conditions for simultaneous stabilization of three linear systems within the framework of nest algebras. Journal of the Franklin Institute 351, 5310–5325 (2014) – 10.1016/j.jfranklin.2014.09.001
Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
Sun, L. & Wang, Y. Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method. Sci. China Ser. F-Inf. Sci. 52, 2140–2152 (2009) – 10.1007/s11432-009-0181-y
Wei, A., Wang, Y. & Hu, X. Adaptive simultaneous stabilization of two Port-Controlled Hamiltonian systems subject to actuator saturation. Proceedings of the 10th World Congress on Intelligent Control and Automation 1767–1772 (2012) doi:10.1109/wcica.2012.6358163 – 10.1109/wcica.2012.6358163
Wei, A. & Wang, Y. Adaptive parallel simultaneous stabilization of a set of uncertain port‐controlled hamiltonian systems subject to actuator saturation. Adaptive Control & Signal 28, 1128–1144 (2013) – 10.1002/acs.2433
Cao, Z. & Hou, X. Robust Simultaneous Stabilization Control Method for Two Port-Controlled Hamiltonian Systems: Controller Parameterization. Abstract and Applied Analysis 2014, 1–8 (2014) – 10.1155/2014/748930
Schaft A., L2 ‐gain and Passivity in Nonlinear Control (1999)
Shen T., H∞ Control Theory and its Applications (1996)
Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
Wang, Y., Cheng, D. & Ge, S. S. Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions. Systems & Control Letters 56, 141–149 (2007) – 10.1016/j.sysconle.2006.08.005
Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 1996). doi:10.1007/3-540-76074-1 – 10.1007/3-540-76074-1
Quantifier Elimination and Cylindrical Algebraic Decomposition. Texts and Monographs in Symbolic Computation (Springer Vienna, 1998). doi:10.1007/978-3-7091-9459-1 – 10.1007/978-3-7091-9459-1
Swamy, K. On Sylvester’s criterion for positive-semidefinite matrices. IEEE Trans. Automat. Contr. 18, 306–306 (1973) – 10.1109/tac.1973.1100319