DOI QR코드

DOI QR Code

An Output Feedback Predictive Control for Stabilizing a System With Multiple Delayed Inputs

지연된 다중 입력을 갖는 시스템을 안정화하는 출력 궤환 예측 제어

  • Yang, Janghoon (Department of New Media, Seoul Media Institute of Technology)
  • 양장훈 (서울미디어대학원대학교 뉴미디어학부)
  • Received : 2019.09.03
  • Accepted : 2019.10.26
  • Published : 2019.10.31

Abstract

The evolution of networking technology such as commercialization of 5G systems provides foundation for information exchange and control of systems over the network. In addition, importance of controlling a system with delay is increasing significantly, since various phenomena in the network are associated with delay. In this paper, with a predictive control which has been studied for designing a controller with low complexity, we propose a novel predictive control for a system with multi-inputs such that it can keeps the complexity almost the same regardless of the number of inputs and degree of delay. The asymptotic stability of the proposed control with a static output feedback is also proved. The numerical simulation shows that the proposed method is superior in complexity and the performance of finding feasible controllers to the existing predictive control and a conventional method based on augmented states.

5G의 상용화 등 네트워킹 기술의 발전은 다양한 시스템들이 네트워크를 통해서 정보를 교환하고 제어할 수 있는 기반을 제공하고 있다. 또한, 네트워크에서 발생하는 많은 현상들은 정보의 지연과 관련되기 때문에 지연된 정보를 갖는 시스템의 제어의 중요성이 증가하고 있다. 본 논문에서는 최근들어 지연이 있을 때에 저복잡도 제어기 설계에 많이 활용되는 예측 제어를 도입하여, 지연된 다중 입력을 갖는 시스템에서 지연의 크기와 입력의 수에 상관없이 거의 일정한 복잡도를 갖는 예측 제어기를 제시한다. 또한, 출력 궤환 구조를 갖는 예측 제어기가 점근적 수렴이 보장됨을 증명한다. 모의 실험을 통해서 제안된 방식이 상태 벡터를 확장한 전통적인 방식이나, 다른 예측 기반 제어 방식에 비해 적은 복잡도를 가지면서 안정성을 보장하는 제어기 설계 성공이 높게 발생함을 확인하였다.

Keywords

References

  1. E. G. W. Peters, D. E. Quevedo, and M. Fu, “Controller and scheduler codesign for feedback control over IEEE 802.15.4 networks,” IEEE Transactions on Control Systems Technology, Vol. 24, No. 6, pp. 2016-2030, Nov. 2016. https://doi.org/10.1109/TCST.2016.2517571
  2. F. Voigtlander, A. Ramadan, J. Eichinger, C. Lenz, D. Pensky, A. Knoll, "5G for robotics: ultra-low latency control of distributed robotic systems," in Proceeding of International Symposium on Computer Science and Intelligent Controls (ISCSIC), Budapest: Hungary, pp. 69-72, Oct. 2017.
  3. L. Schenato, B. Sinopoli, M. Francescheti, K. Poolla, and S. S. Sastry, "Foundations of control and estimation over lossy networks," Proceedings of IEEE, Vol. 95, No. 1, pp.163-187, Jan. 2007. https://doi.org/10.1109/JPROC.2006.887306
  4. E. Fridman, "Tutorial on Lyapunov-based methods for time-delay systems," European Journal of Control, Vol. 20, pp. 271-283, 2014. https://doi.org/10.1016/j.ejcon.2014.10.001
  5. E. Fridman, "Stability of linear descriptor systems withdelay: a Lyapunov-based approach," Journal of Mathematical Analysis and Applications, Vol. 273, No. 1, pp.24-44, Sep. 2002. https://doi.org/10.1016/S0022-247X(02)00202-0
  6. M. Wu, Y. Hea, J. She, and G. Liu, “Delay-dependent criteria for robust stability of time-varying delay systems,” Automatica, Vol. 40, No. 8, pp. 1435-1439, Aug. 2004. https://doi.org/10.1016/j.automatica.2004.03.004
  7. M. Cloosterman, N. van de Wouw, M. Heemels, and H. Nijmeijer, "Robust stability of networked control systems with time-varying network-induced delays," in Proceeding of IEEE Conference on Decision and Control, San Diego: CA, pp.4980-4985, Dec. 2006.
  8. M. Cloosterman, N. van de Wouw, W.P.M.H. Heemels , and H. Nijmeijer, "Stability of networked control systems with large delays," in Proceeding of IEEE Conference on Decision and Control, New Orleans: LA, pp.5017-5022, Dec. 2007.
  9. F. Rasool, and S. K. Nguang, "Quantized robust $H_{\infty}$ control of discrete-time systems with random communication delays," Journal International Journal of Systems Science, Vol. 42, No. 1, pp. 129-138, Jan. 2011. https://doi.org/10.1080/00207720903470171
  10. J. Yang, "A static output feedback predictive control for a system with multiple input delays," in Proceeding of International Conference on Instrumentation, Control, and Automation, Bandung: Indonesia, pp.1-5,July-Aug. 2019.
  11. B. Zhou, and Z. Lin, "Truncated predictor feedback stabilization of polynomially unstable linear systems with multiple time-varying input delays," IEEE Transactions on Automatic Control, Vol. 59, No. 8, pp. 2157 - 2163, Aug. 2014. https://doi.org/10.1109/TAC.2013.2297188
  12. A. Ponomarev, "Nonlinear predictor feedback for input-affine systems with distributed input delays," IEEE Transactions on Automatic Control, Vol. 61, No. 9, pp. 2591 - 2596, Sept. 2016. https://doi.org/10.1109/TAC.2015.2496191
  13. N. Bekiaris-Liberis, and M. Krstic, "Lyapunov stability of linear predictor feedback for distributed input delays," IEEE Transactions on Automatic Control, Vol. 56, No. 3, pp. 655-660, Mar. 2011. https://doi.org/10.1109/TAC.2010.2092030
  14. S. Y. Yoon, and Z Lin, “Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay,” Systems & Control Letters, Vol. 62, No. 10, pp. 837-844, Oct. 2013. https://doi.org/10.1016/j.sysconle.2013.05.013
  15. A. Ponomarev, "Reduction-based robustness analysis of linear predictor feedback for distributed input delays," IEEE Transactions on Automatic Control, Vol. 61, No. 2, pp. 468-472, Feb. 2016. https://doi.org/10.1109/TAC.2015.2437520
  16. L. E. Ghaoui, F. Oustry, and M. AitRami, “A cone complementarity linearization algorithm for static output-feedback and related problems,” IEEE Transactions on Automatic Control, Vol. 42, No. 8, pp. 1171-1176, Aug. 1997. https://doi.org/10.1109/9.618250