Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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A Frozen Time Receding Horizon Control for a Linear Discrete Time-Varying System

선형 이산 시변시스템을 위한 고정시간 이동구간 제어

  • Published : 2010.02.01
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Abstract

In the case of a linear time-varying system, it is difficult to apply the conventional stability conditions of RHC (Receding Horizon Control) to real physical systems because of computational complexity comes from time-varying system and backward Riccati equation. Therefore, in this study, a frozen time RHC for a linear discrete time-varying system is proposed. Since the proposed control law is obtained by time-invariant Riccati equation solved by forward iterations at each control time, its stability can be ensured by matrix inequality condition and the stability condition based on horizon for a time-invariant system, and they can be applied to real physical systems effectively in comparison with the conventional RHC.

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References

  1. W. H. Kwon and A E. Pearson, "A modified quadratic cost problem and feedback stabilization of a linear system," IEEE Transactions on Automatic Control, vol. 22, pp. 838-842, 1977. https://doi.org/10.1109/TAC.1977.1101619
  2. G. D. Nicolao and S. Strada, "On the stability of receding-horizon LQ control with zero-state terminal constraint," IEEE Transactions on Automatic Control, vol. 42, pp. 257-260,1997. https://doi.org/10.1109/9.554406
  3. W. H. Kwon and K.B. Kim, "On stabilizing receding horizon controls for linear continuous time-invariant systems," IEEE Transactions on Automatic Control, vol. 45, pp. 1329-1334, 2000. https://doi.org/10.1109/9.867037
  4. J. W. Lee, W. H. Kwon, and J. H. Choi, "On stability of constrained receding horizon control with finite terminal weighting matrix," Automatica, vol. 34, no.12, pp. 1607-1612, 1998. https://doi.org/10.1016/S0005-1098(98)80015-0
  5. M. H. Oh and J. H. Oh, "On the stability of receding horizon control based on horizon size," IEICE Transactions on Fundamentals, vol. E87-A, no. 2, pp. 505-508, 2004.
  6. M. H. Oh and J. H. Oh, "On the stability of receding horizon control for linear discrete systems based on horizon size," submitted to JMST, 2009.
  7. Z. Quart S. B. Ran, and W. H. Kwon, "Stability-guaranteed horizon size for receding horizon control," IEICE Transactions on Fundamentals, vol. E90-A, no. 2, pp. 523-525, 2007. https://doi.org/10.1093/ietfec/e90-a.2.523
  8. H. K. Wimmer and M. Pavon, "A comparison theorem for matrix riccati difference equations," System and Control Letters, vol. 19, pp. 233-239, 1992. https://doi.org/10.1016/0167-6911(92)90118-C
  9. E. DE Souza, "On stabilizing properties of solutions of the Riccati difference equation," IEEE Transactions on Automatic Control, vol. 34, no. 12, pp. 1313-1316, 1989. https://doi.org/10.1109/9.40787
  10. K. B. Kim, "On stabilizing receding horizon controls for linear systems," Ph D Dissertation, 1999.