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Control and optimization of sampled-data systems with quantization and actuator saturation

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Abstract

This paper is concerned with control and optimization for a sampled-data system with quantization and actuator saturation. Based quantization and actuator saturation a controller is introduced. The corresponding closed loop system is transformed into a system with input saturation and bounded external disturbance. A new Lyapunov functional is constructed to derive a sample-interval dependent condition on the existence of a state feedback controller such that the closed-loop system is exponentially convergent to an ultimate ellipsoid for the initial condition starting from some initial ellipsoid. Based on the condition, the desired controller is designed. Furthermore, optimization problems about the sample-interval, the ultimate ellipsoid and the initial ellipsoid are formulated. An example is given to illustrate the effectiveness of the proposed method.

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References

  1. Chen T and Francis B, Optimal Sampled-Data Control Systems, Springer, Berlin, 1995.

    Book  MATH  Google Scholar 

  2. Ghantasala S and El-Farra N, Active fault-tolerant control of sampled-data nonlinear distributed parameter systems, Int. J. Robust Nonlinear Control, 2012, 22(1): 24–42.

    Article  MathSciNet  MATH  Google Scholar 

  3. Van De Wouw N, Naghshtabrizi P, Cloosterman M B G, et al., Tracking control for sampleddata systems with uncertain time-varying sampling intervals and delays, Int. J. Robust Nonlinear Control, 2010, 20(4): 387–411.

    MATH  Google Scholar 

  4. Peng C and Tian Y C, Networked H∞ control of linear systems with state quantization, Information Sciences, 2007, 177(24): 5763–5774.

    Article  MathSciNet  MATH  Google Scholar 

  5. Shao H Y and Han Q L, On stabilization for systems with two additive time-varying input delays arising from networked control systems, J. Franklin Inst., 2012, 349(6): 2033–2046.

    Article  MathSciNet  MATH  Google Scholar 

  6. Fujioka H, Stability analysis of systems with aperiodic sample-and-hold device, Automatica, 2009, 45(3): 771–775.

    Article  MathSciNet  MATH  Google Scholar 

  7. Shao H Y and Zhang Z Q, Delay-dependent state feedback stabilization for a networked control model with two additive input delays, Appl. Math. Comput., 2015, 265: 748–758.

    MathSciNet  Google Scholar 

  8. Suh Y, Stability and stabilization of nonuniform sampling systems, Automatica, 2008, 44(12): 3222–3226.

    Article  MathSciNet  MATH  Google Scholar 

  9. Oishi Y and Fujioka H, Stability and stabilization of aperiodic sampled-data control systems: An approach using robust linear matrix inequalities, Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 8142–8147.

    Google Scholar 

  10. Naghshtabrizi P, Hespanha J P, and Teel A R, Exponential stability of impulsive systems with application to uncertain sampled-data systems, Syst. Control Lett., 2008, 57(5): 378–385.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hu L S, Lam L, Cao Y Y, et al., An LMI approach to robust H2 sampled-data control for linear uncertain systems with time-varying delay, IEEE Trans. Syst. Man Cybern. Part B Cybern., 2003, 33(1): 149–155.

    Article  Google Scholar 

  12. Zhu X L and Wang Y Y, New stability and stabilization criteria for sampled-data systems, Proceedings of the 8th IEEE International Conference on Control and Automation, Xiamen, China, 2010, 1829–1834.

    Google Scholar 

  13. Wen G H, Duan Z S, Yu W W, et al., Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: A delayed-input approach, Int. J. Robust Nonlinear Control, 2013, 23(6): 602–619.

    Article  MathSciNet  MATH  Google Scholar 

  14. Fridman E, A refined input delay approach to sampled-data control, Automatica, 2010, 46(2): 421–427.

    Article  MathSciNet  MATH  Google Scholar 

  15. Shao H Y, New delay-dependent stability criteria for systems with interval delay, Automatica, 2009, 45(3): 744–749.

    Article  MathSciNet  MATH  Google Scholar 

  16. Kim J, Further improvement of Jensen inequality and application to stability of time-delay systems, Automatica, 2016, 64: 121–125.

    Article  MathSciNet  MATH  Google Scholar 

  17. Shao H Y, Lam J, and Feng Z G, Sampling-interval-dependent stability for linear sampled-data systems with nonuniform sampling, Int. J. Syst. Sci., 2016, 47(12): 2893–2900.

    Article  MATH  Google Scholar 

  18. Zuo Z Q, Ho D W C, and Wang Y J, Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation, Automatica, 2010, 46(2): 569–576.

    Article  MathSciNet  MATH  Google Scholar 

  19. Xu S Y, Feng G, Zou Y, et al., Robust controller design of uncertain discrete time-delay systems with input saturation and disturbances, IEEE Trans. Automatic Control, 2012, 57(10): 2604–2609.

    Article  MathSciNet  MATH  Google Scholar 

  20. Seuret A and Da Silva J M G, Taking into account period variations and actuators saturation in sampled-data systems, Syst. Control Lett., 2012, 61(12): 1286–1293.

    Article  MathSciNet  MATH  Google Scholar 

  21. Kalman R, Nonlinear aspects of sampled-data control systems, Proceedings of the Symposium on Nonlinear Circuit Theory, Brooklyn, New York, 1956.

    Google Scholar 

  22. Rasool F, Huang D, and Nguang S, Robust H∞ output feedback control of discrete-time networked systems with limited information, Syst. Control Lett., 2011, 60(10): 845–853.

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu A D, Yu L, Zhang W A, et al., Moving horizon estimation for networked systems with quantized measurements and packet dropouts, IEEE Trans. Circuits Syst. Regul. Pap., 2013, 60(7): 1823–1834.

    Article  MathSciNet  Google Scholar 

  24. Zhang D, Yu L, and Zhang W A, Energy efficient distributed filtering for a class of nonlinear systems in sensor networks, IEEE Sens. J., 2015, 15(5): 3026–3036.

    Article  Google Scholar 

  25. Fridman E and Dambrine M, Control under quantization, saturation and delay: An LMI approach, Automatica, 2009, 45(10): 2258–2264.

    Article  MathSciNet  MATH  Google Scholar 

  26. Gao H J and Chen T, H∞ estimation for uncertain systems with limited communication capacity, IEEE Trans. Automatic Control, 2007, 52(11): 2070–2084.

    Article  MathSciNet  MATH  Google Scholar 

  27. Ishido Y, Takaba K, and Quevedo D E, Stability analysis of networked control systems subjected to packet-dropouts and finite-level quantization, Syst. Control Lett., 2011, 60(5): 325–332.

    Article  MATH  Google Scholar 

  28. Shao H Y, Han Q L, Zhang Z Q, et al., Sampling-interval-dependent stability for sampled-data systems with state quantization, Int. J. Robust Nonlinear Control, 2014, 24(17): 2995–3008.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Automation, Qufu Normal University, Qufu, 273165, China

    Hanyong Shao & Jianrong Zhao

Authors
  1. Hanyong Shao
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  2. Jianrong Zhao
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Correspondence to Hanyong Shao.

Additional information

This research was partially supported by the Natural Science Foundation of China under Grant Nos. 61374090, and 61473171, the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province, and the Taishan Scholarship Project of Shandong Province.

This paper was recommended for publication by Editor SUN Jian.

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Shao, H., Zhao, J. Control and optimization of sampled-data systems with quantization and actuator saturation. J Syst Sci Complex 30, 1242–1257 (2017). https://doi.org/10.1007/s11424-017-6083-y

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  • DOI: https://doi.org/10.1007/s11424-017-6083-y

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