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A Relaxed Observer-Based Control for LPV Stochastic Systems Subject to H∞ Performance

  • Guan-Wei Chen
  • Cheung-Chieh KuEmail author
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Abstract

A relaxed observer-based control problem of the disturbed Linear Parameter Varying (LPV) stochastic systems is addressed in this paper. For the control problem, some sufficient conditions are derived via a Lyapunov function whose positive definite matrix is not required as the diagonal case. Besides, a general H∞ performance index is proposed to constrain the effect of external disturbance on the state and estimation error. Furthermore, a lemma is proposed to eliminate the oscillation caused by determining performance level of state and estimation error. Another lemma is developed via extending projection lemma to convert the derived conditions into strict Linear Matrix Inequality (LMI) form. By using convex optimization algorithm, all feasible solutions can be obtained by a single-step calculation to establish an observer-based Gain-Scheduled (GS) controller. Based on the designed controller, the asymptotical stability and H∞ performance of the LPV stochastic systems can be guaranteed in the sense of mean square. Finally, two examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Keywords

Gain scheduled control H∞ performance LPV system multiplicative noise observer-based control 
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References

  1. [1]
    D. Rotondo, F. Nejjari, and V. Puig, “Robust state-feedback control of uncertain LPV systems: an LMI-based approach,” Journal of the Franklin Institute, vol. 351, no. 5, pp. 2781–2803, 2014.MathSciNetCrossRefGoogle Scholar
  2. [2]
    C. C. Ku and C. I. Wu, “Controller synthesis of linear parameter varying stochastic systems based on gainscheduled technique,” Journal of the Chinese Institute of Engineers, vol. 39, no. 3, pp. 274–281, 2016.CrossRefGoogle Scholar
  3. [3]
    M. G. Yoon, V. A. Ugrinovskii, and M. Pszczel, “Gainscheduling of minimax optimal state-feedback controllers for uncertain LPV systems,” IEEE Trans. on Automatic Control, vol. 52, no. 2, pp. 311–317, 2007.MathSciNetCrossRefGoogle Scholar
  4. [4]
    N. Wada, K. Saito, and M. Saeki, “Model predictive control for linear parameter varying systems using parameter dependent Lyapunov function,” IEEE Trans. on Circuits and Systems II: Express Briefs, vol. 53, no. 12, pp. 1446–1450, 2006.CrossRefGoogle Scholar
  5. [5]
    M. Sato, “Gain-scheduled open-loop system design for LPV systems using polynomially parameter-dependent Lyapunov functions,” Systems and Control Letters, vol. 59, no. 5, pp. 265–276, 2010.MathSciNetCrossRefGoogle Scholar
  6. [6]
    W. Xie, “Gain scheduled state feedback for LPV system with new LMI formulation,” IEEE Proc., Part D, Control Theory and Application, vol. 152, no. 6, pp. 693–697, 2005.CrossRefGoogle Scholar
  7. [7]
    I. E. Kose, F. Jabbari, and W. E. Schmitendorf, “A direct characterization of L 2-gain controllers for LPV systems,” IEEE Trans. on Automatic Control, vol. 43, no. 9, pp. 1302–1307, 1998.MathSciNetCrossRefGoogle Scholar
  8. [8]
    C. C. Ku and C. I. Wu, “Gain-scheduled H ∞ control for linear parameter varying stochastic systems,” ASME, Journal of Dynamic Systems, Measurement and Control, vol. 137, no. 11, 111012 (12pages), 2015.CrossRefGoogle Scholar
  9. [9]
    S. Zhang, J. J. Yang and G. G. Zhu, “LPV modeling and mixed constrained H 2/H ∞ control of an electronic throttle,” IEEE/ASME Trans. on Mechatronics, vol. 20, no. 5, pp. 2120–2132, 2015.CrossRefGoogle Scholar
  10. [10]
    J. Wang and Y. Wei, “Observer-based gain-scheduled H ∞ control for LPV systems with time-varying delays,” Proc. of the IEEE 2nd Int. Symposium on Systems and Control in Aerospace and Astronautics, pp. 1–7, 2008.Google Scholar
  11. [11]
    W. P. Maurice, H. Heemels, J. Daafouz, and G. Millerioux, “Observer-based control of discrete-time LPV systems with uncertain parameters,” IEEE Trans. on Automatic Control, vol. 55, no. 9, pp. 2130–2135, 2010.MathSciNetCrossRefGoogle Scholar
  12. [12]
    C. C. Ku and G. W. Chen, “Relaxed observer-based controller design method of discrete-time multiplicative noised LPV systems via an extended projective lemma,” Int. Journal of Control, 2018. DOI:  https://doi.org/10.1080/00207179.2018.1476983
  13. [13]
    D. Efimov, T. Raïssi, and A. Zolghadri, “Control of nonlinear and LPV systems: interval observer-based framework,” IEEE Trans. on Automatic Control, vol. 58, no. 3, pp. 773–778, 2013.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Y. Liu, X. Ban, F. Wu, and H. K. Lam, “A gain-scheduling control approach for Takagi-Sugeno fuzzy systems based on linear parameter-varying control theory,” ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 138, no. 1, 011008 (9 pages), 2016.CrossRefGoogle Scholar
  15. [15]
    J. Song, Y. Niu, J. Lam, and Z. Shu, “A hybrid design approach for output feedback exponential stabilization of Markovian jump systems,” IEEE Trans. on Automatic Control, vol. 63, no. 5, 1404–1417, 2018.MathSciNetCrossRefGoogle Scholar
  16. [16]
    L. Zhou, J. She, and S. Zhou, “Robust H ∞ control of an observer-based repetitive-control system,” Journal of the Franklin Institute, vol. 355, no. 12, pp. 4952–4969, 2018.MathSciNetCrossRefGoogle Scholar
  17. [17]
    J. C. Silva-Rivas and W. J. Kim, “Multivariable control and optimization of a compact 6-DOF precision positioner with hybrid H 2/H ∞ and digital filtering,” IEEE Trans. on Control Systems Technology, vol. 21, no. 5, pp. 1641–1651, 2012.CrossRefGoogle Scholar
  18. [18]
    E. Allen, Modelling with Itô Stochastic Differential Equations, Springer, Texas, 2007.zbMATHGoogle Scholar
  19. [19]
    W. J. Chang, H. Y. Qiao, and C. C. Ku, “Sliding mode fuzzy control for nonlinear stochastic systems subject to pole assignment and variance constraint,” Information Sciences, vol. 432, pp. 133–145, 2018.MathSciNetCrossRefGoogle Scholar
  20. [20]
    W. J. Chang, P. H. Chen, and C. C. Ku, “Variance and passivity constrained sliding mode fuzzy control for continuous stochastic nonlinear systems,” Neurocomputing, vol. 201, pp. 29–39, 2016.CrossRefGoogle Scholar
  21. [21]
    J. Song and Y. Niu, “Resilient finitetime stabilization of fuzzy stochastic systems with randomly occurring uncertainties and randomly occurring gain fluctuations,” Neurocomputing, vol.171, pp. 444–451, 2016.CrossRefGoogle Scholar
  22. [22]
    J. Li, Q. Zhang, X. G. Yan, and S. K. Spurgeon, “Robust stabilization of T-S fuzzy stochastic descriptor systems via integral sliding modes,” IEEE Trans. on Cybernetics, vol. 48, no. 9, pp. 2736–2749, 2018.CrossRefGoogle Scholar
  23. [23]
    X. L. Lin, C. F. Wu, and B. S. Chen, “Robust H ∞ adaptive fuzzy tracking control for MIMO nonlinear stochastic Poisson jump diffusion systems,” IEEE Trans. on Cybernetics, vol. 49, no. 8, pp. 3116–3130, 2018.CrossRefGoogle Scholar
  24. [24]
    C. Yuan and X. Mao, “Robust stability and controllability of stochastic differential delay equations with Markovian switching,” Automatica, vol. 40, no. 3, pp. 343–354, 2004.MathSciNetCrossRefGoogle Scholar
  25. [25]
    V. A. Ugrinovskii, “Robust H ∞ control in the presence of stochastic uncertainty,” Int. Journal of Control, vol. 71, no. 2, pp. 219–237, 1998.MathSciNetCrossRefGoogle Scholar
  26. [26]
    S. Kong, M. Saif, and H. Zhang, “Optimal filtering for Itô stochastic continuous-time systems with multiple delayed measurements,” IEEE Trans. on Automatic Control, vol. 58, no. 7, pp. 1872–1877, 2013.MathSciNetCrossRefGoogle Scholar
  27. [27]
    J. Song, Y. Niu, and Y. Zou, “A parameter-dependent sliding mode approach for finite-time bounded control of uncertain stochastic systems with randomly varying actuator faults and its application to a parallel active suspension system,” IEEE Trans. on Industrial Electronics, vol. 65, no. 10, pp. 8124–8132, 2018.CrossRefGoogle Scholar
  28. [28]
    H. Gassara, A. El Hajjaji, and M. Chaabane, “Observer-based robust H ∞ reliable control for uncertain T-S fuzzy systems with state time delay,” IEEE Trans. on Fuzzy Systems, vol. 18, no. 6, pp. 1027–1040, 2010.CrossRefGoogle Scholar
  29. [29]
    M. Wu, L. Zhou, and J. She, “Design of observer-based H ∞ robust repetitive-control system,” IEEE Trans. on Automatic Control, vol. 56, no. 6, pp. 1452–1457, 2011.MathSciNetCrossRefGoogle Scholar
  30. [30]
    H. Qu and F. Yang, “Distributed H ∞-consensus filtering for target tracking over a wireless filter network with switching topology, channel fading and packet dropouts,” Neurocomputing, in press, 2019.Google Scholar
  31. [31]
    S. Ahmad and M. Rehan, “On observer-based control of one-sided Lipschitz systems,” Journal of the Franklin Institute, vol. 353, no. 4, pp. 903–916, 2016.MathSciNetCrossRefGoogle Scholar
  32. [32]
    Y. Boukal, M. Darouach, M. Zasadzinski, and N. E. Radhy, “Robust H ∞observer-based control of fractional-order systems with gain parametrization,” IEEE Trans. on Automatic Control, vol. 62, no. 11, pp. 5710–5723, 2017.MathSciNetCrossRefGoogle Scholar
  33. [33]
    H. N. Wu, “Disturbance observer based robust mixed H 2/H ∞ fuzzy tracking control for hypersonic vehicles,” Fuzzy Sets and Systems, vol. 306, pp. 118–136, 2016.CrossRefGoogle Scholar
  34. [34]
    H. Zhang, Q. Hong, H. Yan, and Y. Luo, “Observer-based decentralized event-triggered H ∞ control for networked systems,” Journal of the Franklin Institute, vol. 354, no. 9, pp. 3744–3759, 2017.MathSciNetCrossRefGoogle Scholar
  35. [35]
    H. Huang, T. Huang and X. Chen, “Further result on guaranteed performance state estimation of delayed static neural networks,” IEEE Trans. on Neural Networks and Learning Systems, vol. 26, no. 6, pp. 1335–1341, 2015.MathSciNetCrossRefGoogle Scholar
  36. [36]
    C. S. Tseng, “A novel approach to H ∞ decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems,” IEEE Trans. on Fuzzy Systems, vol. 16, no. 5, pp. 1337–1350, 2008.CrossRefGoogle Scholar
  37. [37]
    H. Zhang, Q. Wei, and Y. Luo, “A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 38, no. 4, pp. 937–942, 2008.CrossRefGoogle Scholar
  38. [38]
    J. Li, Q. Zhang, X. G. Yan, and S. K. Spurgeon, “Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems,” IEEE Trans. on Fuzzy Systems, vol. 26, no. 5, pp. 2818–2832, 2018.CrossRefGoogle Scholar
  39. [39]
    P. Apkarian, H. D. Tuan, and J. Bernussou, “Continuous-time analysis, eigenstructure assignment, and H 2 synthesis with enhanced linear matrix inequalities (LMI) characterizations,” IEEE Trans. on Automatic Control, vol. 46, no. 12, pp. 1941–1946, 2001.MathSciNetCrossRefGoogle Scholar
  40. [40]
    S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.CrossRefGoogle Scholar
  41. [41]
    Y. Liu, C. Guo, and S. Yuan, “Integrated LPV control for underactuated ship linear track keeping and main diesel engine,” Proc. of the IEEE 7th World Congress on Intelligent Control and Automation, pp. 1840–1845, 2008.Google Scholar
  42. [42]
    J. Qiu, Y. Wei, H. R. Karimi, and H. Gao, “Reliable control of discrete-time piecewise-affine time-delay systems via output feedback,” IEEE Trans. on Reliability, vol. 67, no. 1, pp. 79–91, 2018.CrossRefGoogle Scholar
  43. [43]
    J. Qiu, K. Sun, T. Wang, and H. Gao, “Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance,” IEEE Trans. on Fuzzy Systems, 2019. DOI:  https://doi.org/10.1109/TFUZZ.2019.2895560 CrossRefGoogle Scholar
  44. [44]
    J. Li and Q. Zhang, “Fuzzy reduced-order compensator-based stabilization for interconnected descriptor systems via integral sliding modes,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, vol. 49, no. 4, pp. 752–765, 2017.CrossRefGoogle Scholar

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© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.Department of Marine EngineeringNational Taiwan Ocean UniversityKeelung CityTaiwan

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